Cardinality estimation for subgraph matching is a crucial task in graph query optimization. The state-of-the-art cardinality estimation algorithm FaSTest can provide accurate estimations within a short time frame. However, it is a serial algorithm and its efficiency is limited by the performance of a single core. In this work, we present a parallel approach to accelerate FaSTest using multi-threaded parallelism. In the indexing phase, we propose a nested granularity partitioning algorithm to balance workloads skewed by power-law degree distributions during the four-cycle indexing step. In the query processing phase, we introduce data-parallel candidate space refinement and graph sampling algorithms with thread binding to minimize task switching overheads. Experiments on six real-world datasets demonstrate that our parallel implementation maintains FaSTest’s accuracy while achieving the maximum speedup ratios of 1.53x - 6.93x and 1.13x - 4.61x on the indexing and query processing phase, respectively.