In the present paper we propose a new stochastic diffusion process with drift proportional to the Weibull density function defined as X $ε$ = x, dX t = $γ$ t (1 - t $γ$+1) - t $γ$ X t dt + $σ$X t dB t , t \textgreater{} 0, with parameters $γ$ \textgreater{} 0 and $σ$ \textgreater{} 0, where B is a standard Brownian motion and t = $ε$ is a time proche to zero. First we interested to probabilistic solution of this process as the explicit expression of this process. By using the maximum likelihood method and by considering a discrete sampling of the sample of the new process we estimate the parameters $γ$ and $σ$.