In the present paper, we approach the stochastic Gompertz diffusion process (SGDP) from the point of view of Itô's stochastic differential equations. The stochastic model is solved analytically by applying Itô's calculus and the mean value of the proposed process is calculated. The parameter estimators are then derived by means of two procedures: the first is used to estimate the parameters in the drift coefficient by the maximum likelihood principle, based on continuous sampling, and the second procedure approximates the diffusion coefficient. Finally, a simulation of the process is presented. Thus, a typical simulated trajectory of the process and its estimators is obtained.