The Weibull-Geometric (WG) distribution was first introduced by Wagner Barreto-Souzaa, Alice Lemos de Moraisa and Gauss M. Cordeiro in (2011). This distribution generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998).It is useful for modeling unimodal failure rates. The WG distribution can be used as a life-time model. In this paper, we deal with the problem of estimating the parameters of the Weibull-Geometric distribution based on progressive first-failure censoring scheme. The maximum likelihood and Bayes methods of estimation are used for this purpose. The Monte Carlo Integration (MCI) technique is used for computing the Bayes estimates. The Bayes estimates of the parameters are compared with their corresponding maximum likelihood estimates via Monte Carlo simulation study.