Abstract: The concept of local derivations from Lie algebra to adjoint module was extended to any finite dimensional module. The problem of solving the local derivations of the general linear Lie algebra sl(2,C) to any simple module was equivalently transformed into solving the related linear equations. By using the rank of the coefficient matrix was equal to the rank of the augmented matrix, the local derivation spaces from 3-dimensional simple Lie algebra sl(2,C) to two kinds of simple modules V(3) and V(4) were determined.

Key words: Lie algebra, simple module, local derivation, rank