Hi abhishek_kumar371,


using below vf page,
--> We can change the record type if account is already created
--> We can create select a new record type while creating an Account.
Override the new & edit buttons with below visualforce page. 

Create two record types for Account object as "Record Type 1" and "Record Type 2" before using the below code

Visualforce page:
<apex:page standardController="Account" extensions="AccountRecordTYpeCtr">
    <apex:form >
        <apex:pageBlock mode="edit" >
            <apex:pageBlockButtons >
                <apex:commandButton value="Save" action="{!Save}"  />
            </apex:pageBlockButtons>
            <apex:messages />
            <apex:pageBlockSection title="Record Type Information" >
                    <apex:pageBlockSectionItem >
                        <apex:outputLabel value="Record Types" />
                        <apex:selectList value="{!Account.RecordTypeID}" multiselect="false" size="1" >
                            <apex:selectOptions value="{!RecordTypes}" />
                        </apex:selectList>
                      </apex:pageBlockSectionItem>  
                      <apex:pageBlockSectionItem rendered="{!Account.RecordTypeID!=null}">
                        <apex:outputLabel value="Record Type" />
                        <apex:outputText value="{!Account.RecordType.Name}"/>
                      </apex:pageBlockSectionItem> 
              </apex:pageBlockSection>
                        <apex:pageBlockSection title="Account Information">
                <apex:inputField value="{!Account.Name}"/>
                
                <apex:inputField value="{!Account.Type}"/>
                <apex:inputField value="{!Account.Industry}"/>
                <apex:inputField value="{!Account.AccountNumber}"/>           
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>

Controller:

public class AccountRecordTYpeCtr{
    Account accObj;
    ApexPages.StandardController controller;
    public AccountRecordTYpeCtr(ApexPages.StandardController controller) {
        this.controller = controller;
        accObj = (Account) Controller.getRecord();
    }
    public list<SelectOption> getRecordTypes() {
        list<SelectOption> options = new list<SelectOption>();
        options.add(new SelectOption('', '--None--'));
        for (list<RecordType> recordTypes : [SELECT ID, name FROM RecordType WHERE SObjectType = 'Account' ORDER BY name]) {
            for (RecordType rt : recordTypes) {
                options.add(new SelectOption(rt.ID, rt.Name));
            } 
        }
        return options;
    }
}

After clicking on Edit button: For existing record



After clicking on new button: For New record.



Please mark it as Best Answer if it is solved your problem.
Thank You,
Sohel Mohd