Hi  Siva Kumar,

Use the following sample code to upload a new attachements to Account object record. You can either keep this vf page as inline VF in Account object (or) directly run the page with Id mentioned like https://c.na15.visual.force.com/apex/MultipleFilesUpload?id=001XXXXXXXXXXXXX (/). You can choose how many number of attachment you would like to add to particular record usign this code.

VF page

<apex:page standardController="Account" extensions="MultipleUploadController">
    <apex:form >
        <apex:pageBlock title="Upload Multiple Attachment to Object">
            
            <apex:pageBlockButtons >
                <apex:commandButton value="Upload"  action="{!SaveAttachments}"/>
            </apex:pageBlockButtons>
            
            <apex:pageMessages id="MSG"/>
            <apex:actionFunction name="ChangeCount" action="{!ChangeCount}"/>
            
            <apex:pageblocksection >
                            
                <apex:pageBlockSectionItem >
                    <apex:outputLabel value="How many files you want to upload?"/>
                    <apex:selectList onchange="ChangeCount() ;" multiselect="false" size="1" value="{!FileCount}">
                        <apex:selectOption itemLabel="--None--" itemValue=""/>
                        <apex:selectOptions value="{!filesCountList}"/>
                    </apex:selectList>
                </apex:pageBlockSectionItem>
            
            </apex:pageblocksection>
            
            <apex:pageBlockSection title="Select Files" rendered="{!IF(FileCount != null && FileCount != '', true , false)}">
                <apex:repeat value="{!allFileList}" var="AFL">
                    <apex:inputfile value="{!AFL.body}" filename="{!AFL.Name}" />
                    

                </apex:repeat>
            </apex:pageBlockSection>
            
        </apex:pageBlock>
    </apex:form>
</apex:page>

Controller

public class MultipleUploadController
{   
    //Picklist of tnteger values to hold file count
    public List<SelectOption> filesCountList {get; set;}
    //Selected count
    public String FileCount {get; set;}
    
    public List<Attachment> allFileList {get; set;}
    
    public MultipleUploadController(ApexPages.StandardController controller)
    {
        //Initialize  
        filesCountList = new List<SelectOption>() ;
        FileCount = '' ;
        allFileList = new List<Attachment>() ;
        
        //Adding values count list - you can change this according to your need
        for(Integer i = 1 ; i < 11 ; i++)
            filesCountList.add(new SelectOption(''+i , ''+i)) ;
    }
    
    public Pagereference SaveAttachments()
    {
        String accId = System.currentPagereference().getParameters().get('id');
        if(accId == null || accId == '')
            ApexPages.addmessage(new ApexPages.message(ApexPages.Severity.ERROR,'No record is associated. Please pass record Id in parameter.'));
        if(FileCount == null || FileCount == '')
            ApexPages.addmessage(new ApexPages.message(ApexPages.Severity.ERROR,'Please select how many files you want to upload.'));

        List<Attachment> listToInsert = new List<Attachment>() ;
        
        //Attachment a = new Attachment(parentId = accid, name=myfile.name, body = myfile.body);
        for(Attachment a: allFileList)
        {
            if(a.name != '' && a.name != '' && a.body != null)
                listToInsert.add(new Attachment(parentId = accId, name = a.name, body = a.body)) ;
        }
        
        //Inserting attachments
        if(listToInsert.size() > 0)
        {
            insert listToInsert ;
            ApexPages.addmessage(new ApexPages.message(ApexPages.Severity.INFO, listToInsert.size() + ' file(s) are uploaded successfully'));
            FileCount = '' ;
        }
        else
            ApexPages.addmessage(new ApexPages.message(ApexPages.Severity.ERROR,'Please select at-least one file'));
            
        return null;
    }
    
    public PageReference ChangeCount()
    {
        allFileList.clear() ;
        //Adding multiple attachments instance
        for(Integer i = 1 ; i <= Integer.valueOf(FileCount) ; i++)
            allFileList.add(new Attachment()) ;
        return null ;
    }
}

Hope this helps you. Please select this as a Best answer to give kudos, if it suits your requirment so others can make use of it...!

Regards,
Kamatchi Devi R
Salesforce Certified Developer | Salesforce Certified Administrator | Service Cloud Consultant