Ordinary differential equations (ODE) have been widely used for modeling and analysis of dynamic gene networks in systems biology. In this paper, we propose an optimization method that can infer a gene regulatory network from time-series gene expression data. Specifically, the following four cases are considered: (1) reconstruction of a gene network from synthetic gene expression data with noise, (2) reconstruction of a gene network from synthetic gene expression data with time-delay, (3) reconstruction of a gene network from synthetic gene expression data with noise and time-delay, and (4) reconstruction of a gene network from experimental time-series data in budding yeast cell cycle.