Fluorescence recovery after photobleaching (FRAP) has been extensively used for monitoring the binding kinetics of proteins with a goal to investigate the cellular processes, such as transcriptional regulation, cell membrane diffusion and signal transduction. In this study, a new approach for the interpretation of FRAP curves is presented based on the stochastic simulation of binding kinetics. The proposed method considers that proteins (a) randomly diffuse in a Brownian random-walk manner and (b) react with certain probability with compatible empty binding sites in a homogeneous well-stirred chemical environment. The proposed algorithm was compared with standard deterministic methods that are currently being used for analysis of FRAP curves. Predictions of recovery times of FRAP curves and sum of residuals revealed a good agreement. The stochastic simulation algorithm presents a firmer physical basis than its deterministic counterparts and it might be used to successfully model probabilistic events in the cell, deciphering information in FRAP experiments that cannot be computed using deterministic models.