This paper builds a convergence analysis of explicit tau-leaping schemes for simulat-ing chemical reactions from the viewpoint of stochastic differential equations. Mathematically, thechemical reaction process is a pure jump process on a lattice with state-dependent intensity. Thestochastic differential equation form of the chemical master equation can be given via Poisson ran-dom measures. Based on this form, different types of tau-leaping schemes can be proposed. In orderto make the problem well-posed, a modified explicit tau-leaping scheme is considered. It is shownthat the mean square strong convergence is of order 1/2 and the weak convergence is of order 1 forthis modified scheme. The novelty of the analysis is to handle the non-Lipschitz property of thecoefficients and jumps on the integer lattice.