With the help of J.-E. Pin answer I think I have found another way to solve my problem.
From An introduction to Formal Languages and Automata (fifth edition), we have a theorem.
Theorem: For every CFL L with lambda not in L, there exists a context free grammar G in Griebach Normal Form such that L = L(G)
Now let G = (V,T,S,P) be the grammar in Griebach Normal Form,
where V is set of variables
where T is set of terminals
where S is the start state
where P is set of productions
we have one or more productions in P of the form:
(all the productions that start from S)
S $\to$ aX, where a is a terminal and X $\in$ ${T^*}$
Now make S' exactly the same as S but replace the character symbol with lambda, and S' the new start state, which are production P'.
Add S' and P' to G making G'
Thus G' = (V$\cup$S',T,S', P$\cup$P') will accept the set of string obtained by dropping the first symbol.