Facility layout is one of the most important Operations Management problems due to its direct impact on the financial performance of both private and public firms. Facility layout problem (FLP) with stochastic parameters, unequal area facilities, and grid system modeling is named GSUA-STFLP. This problem has not been worked in the literature so that to solve GSUA-STFLP is our main contribution. In this paper, we have first presented an integer nonlinear programming model which aims to minimize the cost of material handling. Then, a metaheuristic SA-based algorithm is proposed. Our proposed SA is able to generate feasible solutions by a local search operator to explore and exploit the solution space. Next, problems with different sizes besides the real case study have been solved. The computational results show the capability of the proposed SA to obtain the solutions with high quality in a short time.