In this paper, we are interested in the application of the theory of stochastic and mixed effects models on the Geometric Brownian Motion (GBM) with random effect, due to its importance in real studies. Actually, in many modelling studies, it is preferred to consider stochastic processes instead of deterministic, because the majority of real processes are always exposed to influences that are not completely understood or that it is impossible to model explicitly, and ignoring these phenomena in the modelling may affect the estimation result. Moreover, in order to take account of the all population comportment simultaneously, we incorporate two types of parameters in the model: fixed effects to capture general and common behavior for the whole population, and random effects varying between individuals to account for individual deviation. However, the obtained mixed-effects model with stochastic differential equations (SDEs), known by the Stochastic Differential Mixed Effects (SDME) model, is an extremely poorly estimated estimation problem. In fact, in general, the transition density of the stochastic process is usually unknown and therefore the likelihood function cannot be obtained in a closed form. Thus, many numerical approximation methods may be necessary to estimate model parameters. So, here, we consider a framework estimate for the Geometric Brownian Motion incorporating random effect under the Ito formula, by deriving its transition density from the solution of the Fokker-Planck equation.