We present a new method for calculating the time-transient behavior of stochastic reaction networks. We first derive the set of equations for the moments of the master probability distribution. We then linearize these equations calculating the Jacobian matrix around the stationary probability distribution. In order to demonstrate the method, we present examples of stochastic reaction networks and compute their dynamic behavior. We find that the calculations are accurate and significantly more efficient than stochastic simulation algorithms based on Gillespie's algorithms. (c) 2018 Published by Elsevier Ltd.