Monte Carlo methods are often used to solve computational problems with randomness. The random sampling helps avoid the deterministic results, but it requires intensive computations to obtain the results. Several attempts have been made to boost the performance of the Monte Carlo based algorithms by taking advantage of the parallel computers. In this paper, we use the photonic simulation application, MCML, as a case study to 1) parallelize the Monte Carlo method with OpenMP and vectorization, 2) compare the parallelization techniques, and 3) evaluate the parallelized programs on the platforms with the Xeon Phi processor. In particular, the OpenMP version incorporates the vectorization technique that utilizes the AVX-512 vector instructions on the Xeon Phi processor. Our experimental results show that the OpenMP code achieves up to 345x speedup on the Xeon Phi processor, compared with the original code runs on the Xeon E5 processor.