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High-dimensional American option pricing is computationally challenging in both theory and practice. We use stochastic mesh method combined with performance enhancement policy of bias reduction to solve this practical problem in classic Black-Scholes framework. We effectively parallelize this algorithm through splitting the generated mesh by row among processors, use MPI for efficient implementation, and perform large-scale numerical experiments on heterogeneous supercomputer DeepComp7000. Numerical results of parallel simulation demonstrate that parallel simulation has good scalability in different parallel environments of DeepComp7000; large-scale parallel simulation can obtain much better speedup. The convergent performance is also empirically demonstrated. The estimated option value converges with the increase of mesh size; when using smaller mesh size, the stochastic mesh method with bias reduction can underestimate the true American option value. [ABSTRACT FROM AUTHOR]