In this paper, numerical solutions of generalized Huxley equation are obtained by using a new scheme: Implicit logarithmic finite difference method (I-LFDM). The efficiency of the presented method is illustrated by a numerical example for different cases of parameters which confirm that obtained results are in good agreement with the exact solutions and numerical solutions obtained by some other methods in literature. The method is analyzed by von-Neumann stability analysis method and it is displayed that the method is unconditionally stable.