In this paper, the first parallel discrete Gaussian sampler with hierarchical structure is proposed, while keeping statistical distance within the actual distribution. A 3-stage generation strategy is adopted with hierarchical bit search units (BSUs). Except for a high precision BSU at the last stage, several high-speed BSUs that could greatly reduce area consumption of the repeated costly lookup tables are utilized to replace the high-precision BSUs. Moreover, the parallelism of our design provides obfuscation ability against side-channel attacks (SCAs). Results have verified its advantages of area efficiency over the state-of-the-arts (SOAs).