In this paper, we propose an optimization scheme for degree distributions of LDPC codes that combines differential evolution and iterative simplex algorithm. In the proposed scheme, we find good check and variable nodes degree distribution and threshold by using differential evolution, and then, we further optimize check and variable nodes degree distribution that has enhanced code rate by using an iterative simplex algorithm. An iterative simplex algorithm consists of two simplex algorithms, optimizing ρ(x) and λ(x), respectively and iteratively. Some simulation results show that the proposed scheme finds degree distributions, better than those obtained by the differential evolution only, in terms of threshold and/or code rate. As an application of the proposed scheme, we report some new degree distributions with some new maximum degrees.