Thanks Srinivas for your reply..

Code is Working fine bt still for your reference Here is my  code..

Page : 

<apex:page standardController="Accounts__c" id="thePage" extensions="AccountsController">
   
<script type="text/javascript">
       
        function Test() {
          
        
            var account= document.getElementById('{!$Component.thePage.frmAccounts.pb.pbs.account}').value;
                   
          if(account == ''){
                alert('Please select the account');
                return false;   
               }
           
                return true;
        }
       
            </script>

<apex:form id="frmAccounts">
<apex:sectionHeader title="Accounts"/>
   
<apex:pageBlock id="pb">

<apex:pageBlockSection columns="1" id="pbs">


 <apex:selectList size="1" value="{!Accounts__c.Accounts__c}" id="account">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; 
      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
      <b>Accounts</b> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
      <apex:selectOptions value="{!Acc}"/>
     </apex:selectList>

</apex:pageBlockSection>

<apex:pageBlockButtons location="bottom">
     <apex:commandButton value="Save" action="{!Save}" onclick="return Test();">
    
     </apex:commandButton>
</apex:pageBlockButtons>

</apex:pageBlock>

<apex:pageBlock id="pbD">

<apex:pageBlockTable value="{!Accounts}" var="a" id="pbt" align="center" >
         
        <apex:column id="c">
                <apex:facet name="header">Accounts</apex:facet>
                        {!a.Accounts__c}
         </apex:column>
        <apex:column >
                <apex:facet name="header">Action</apex:facet>
                <apex:commandLink value="Delete" action="{!deleteAccount}" >
                <apex:param name="id" value="{!a.id}"/>
                 </apex:commandLink>
         </apex:column>
  
   </apex:pageBlockTable>

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

Controller :

public class AccountsController {

private Accounts__c cntr; 
private final ApexPages.StandardController controller;
private  List<Accounts__c> account{ get; set; }
integer i;   

    public AccountsController(ApexPages.StandardController controller) {
   
    this.controller = controller;

    cntr= (Accounts__c )controller.getRecord();


    }
   
   
   
   
public List<SelectOption> getAcc()
    {
       List<SelectOption> options = new List<SelectOption>();
     
       options.add(new SelectOption('','Select'));      
     
       Schema.DescribeFieldResult fieldResult = Accounts__c.Accounts__c.getDescribe();
      
       List<Schema.PicklistEntry> ple = fieldResult.getPicklistValues();
       
       for( Schema.PicklistEntry f : ple)
       {
          i = [Select count() from Accounts__c where Accounts__c =:f.getValue()];
           if(i==0)
                   {
                     options.add(new SelectOption(f.getLabel(), f.getValue()));
                   }
        
        
       }      
       return options;
    }

   
    
   

 public List<Accounts__c> getAccounts()
    {
     
       account= [Select id, Name, Accounts__c from Accounts__c  ];
       return account;
    }
   
    public PageReference deleteAccount()
    {
        Accounts__c acc= [select id from Accounts__c where id=:ApexPages.currentPage().getParameters().get('id')];
        delete  acc;   
        return null;
    }
    public PageReference Save()
    {
       Accounts__c newAccount = new Accounts__c();
       newAccount.Accounts__c = cntr.Accounts__c;
       insert newAccount ;   
   
       return null;
    }   

}

 Now I have two users A & B.

If A adss any account(record) B sholud not see that record and vice versa.

But in my case When B acess the Account page he is able to see records of his own as well as A's records.

So my question is how to apply record level security so that A cant see B's record n vice versa.

Thanks again for your quick reply..

Do we have to insert owner Id while inserting the record or bydefault it will take the current userid