Bacteria generally live in complicated structures called biofilms, consisting of communicating bacterial colonies and extracellular polymeric substance (EPS). Since biofilms are related to detrimental effects such as infection or antibiotic resistance in different settings, it is essential to model their formation. In this paper, a stochastic model is proposed for biofilm formation, using bacterial quorum sensing (QS). In this model, the biological processes in the biofilm formation are modeled as a chemical reaction network which includes bacterial reproduction, productions of autoinducer and EPS, and their diffusion. The modified explicit tau-leap simulation algorithm is adapted based on the two-state QS mechanism. Our approach is validated by using the experimental results of $\textit{Pseudomonas putida}$ IsoF bacteria for autoinducer and bacteria concentration. It is also shown that the percentage of EPS in the biofilm increases significantly after the state change in QS, while it decreases before QS is activated. The presented work shows how the biofilm growth can be modeled realistically by using the QS mechanism in stochastic simulations of chemical reactions.