The “curse of dimensionality” poses significant difficulties for conventional techniques that seek to directly solve the chemical master equation (CME). This predicament arises when the size of the CME expands exponentially with the number of species, hindering the computation of the full probability distribution of its underlying Markov chain due to the large data generated. The method of moments provides an efficient alternative to circumvent the challenge, in comparison to other well-known approaches such as the stochastic simulation algorithm (SSA) and finite state projection (FSP). However, in circumstances where the full marginal probabilities are needed, it is necessary to have a process by which to reconstruct them from the moments. In this study, we applied the maximum entropy principle to reconstruct the distribution of certain models. This is accomplished using a finite set of moment constraints, enabling us to gain valuable insights into the underlying probability distribution with increased computational efficiency.