The losses during the preparation, propagation, and detection of photons greatly limit the quantum computing advantages of Boson sampling. Boson sampling simulations with four photons and eight modes are realized based on the Clements model using the Markov chain Monte Carlo (MCMC) method to study the influence of photon losses on Boson sampling results in optical networks, and the simulation results are validated and distinguished from the Boson sampling with photon losses at the photon source using the Bayesian test method. The simulation results show that by introducing photon losses based on the optical network, the sampling results obtained using the MCMC method can effectively satisfy the Bayesian test. The number of samples required to satisfy the Bayesian test decreases gradually and tends to be stable when the interval of samples increases. Conversely, as the scale of the optical network increases, the MCMC method requires a larger interval of samples to quickly satisfy the Bayesian test. In this study, Boson sampling with photon losses in optical networks is successfully simulated using MCMC method, giving a clue for Boson sampling researches while considering the errors.