Free energies for various interactions of two-dimensional Ising model with nearest and next nearest interaction are calculated by variational renormalization group transformation which is proposed by Kadanoff et al and modified by Shih ei al. Critical points for various interaction strength ratios are determined. The step by step transformations for points near critical point are examined in detail. The numerical results of these points show clearly that the trajectories are all approach to the fixed point and then off to infinite or zero.