We present a GPU (graphics processing unit) accelerated stochastic algorithm implementation for simulating biochemical reaction networks using the latest NVidia architecture. To effectively utilize the massive parallelism offered by the NVidia Pascal hardware, we apply a set of performance tuning methods and guidelines such as exploiting the architecture's memory hierarchy in our algorithm implementation. Based on our experimentation results as well as comparative analysis using CPU-based implementations, we report our initial experiences on the performance of modern GPUs in the context of scientific computing.