In this paper we present a stochastic formalism to reveal the meso-statistical significance of the entropy and entropy production of finite chemical reaction systems influenced by the Gaussian noise. As an extension of Shanon entropy a generalized stochastic entropy is introduced without missing any information from both internal and external fluctuations coexisting in this kind of system. An explicit expression of the entropy production valid for the steady state affected by the Gaussian white noise has been obtained. It turns out that the contributions of noise to entropy production of the fluctuations are due to the effect that it intensifies the deviations of the effective probability behavior from the Poisson distribution and the central limit theorem. Meanwhile, a nontrivial shift of the Gibbs' entropy production is inevitable if the noise is multiplicative. Finally, as an illustration of the Gaussian colored noise, the influence of the Ornstein-Uhlenbeck noise to entropy production is also discussed. In the very small correlation time limit, it shows similar regularities but in a more complicated and implicit form. An approach to transform the stochastic formalism into a thermodynamic formulation is also mentioned briefly.