Rajesh,

I'm not 100% sure this will solve the problem, but there are two things I suspect of being problematic.

1.  Each time through the loop, you are sending an SMS message to one more mobile number.  That is, the first time through you send one message.  The second time, you send two messages.  The third time, three messages, etc.  It could be a problem to send a message to a number a second time, while the first message is being sent.

2.  You are inserting an individual SMS_History__c record each time through the loop.  This is generally bad form, as you will hit the limit for DML statements if you have more than 100 accounts to process.

I've refactored the code to eliminate these two potential problems.  Try it and see if the error goes away.  I'm eager to know if this helps.

public static void ScheduledSMS()
{
    List<Account> acc = [SELECT Id, Name, Mobile__c from Account where Weekly_Scheduled_SMS__c = true];

    if ( acc.isEmpty() ) return;

    Set<String> sendToPhones = new Set<String>();

    for ( Account a: acc ) sendToPhones.add( a.Mobile__c );

    TwilioMessageHelper.sendSMSMessage( sendToPhones, 'Test SMS' );

    ApexPages.AddMessage( new ApexPages.Message( ApexPages.Severity.INFO, ' SMS has been sent.') );

    List<SMS_History__c> list_SMS_Histories = new List<SMS_History__c>();

    for ( Account a: acc )
    {
        list_SMS_Histories.add
        (   new SMS_History__c
            (   Account__c          = a.Id,
                Message__c          = 'Test SMS ',
                Mobile_Number__c    = a.Mobile__c
            )
        );
    }
    insert list_SMS_Histories;
}

If this helps, please mark it as a solution, and give kudos (click on the star) if you think I deserve them. Thanks!

-Glyn Anderson
Certified Salesforce Developer | Certified Salesforce Administrator