Suppose I have three tables: Tab1(Cola, ,,,,) Tab2(Colb,....), tab3(cola, colb,...)

Cola is primiary key for tab1, colb is primary key for tab2.  Tab3 is a relationship of tab1 and tab2, so cola, colb is foreign keys for tab3.

For tab1 and tabl2, becuase thery are entity, so I can use datacontext db to add a new instance like:

db.Tab1s.InsertOnSubmit( tab1 obj);

db.Save();

db.Tab2s.InsertOnSubmit(tab2 obj);

db.Save();

 But When I try to insert data to tab3 in simiar way:

db.Tab3s.InsertOnSubmit(tab3 obj);

I got exception eroro said that tabl3 has no primiary key.  tab3 only have a index on cola, colb:

-        ex    {"Can't perform Create, Update or Delete operations on 'Table(Tab3)' because it has no primary key."}    System.Exception {System.InvalidOperationException}

How to resolve this issue?

In LINQ to SQL, all your entities should have a primary key column defined. If you don't define an entity without a primary key, you can only fetch its instances from database. You won't be able to make any changes to it. This is mainly because LINQ to SQL uses an Identity-Map to cache and keep track of the entities it is managing.

Check this

http://social.msdn.microsoft.com/Forums/en-US/linqtosql/thread/f3b216d2-fa06-49a1-a901-11702e80b38c