Associative memory plays a crucial role in the cognitive capabilities of the human brain. The Bayesian Confidence Propagation Neural Network (BCPNN) is a cortex model capable of emulating brain-like cognitive capabilities, particularly associative memory. However, the existing GPU-based approach for BCPNN simulations faces challenges in terms of time overhead and power efficiency. In this paper, we propose a novel FPGA-based high performance computing (HPC) design for the BCPNN-based associative memory system. Our design endeavors to maximize the spatial and timing utilization of FPGA while adhering to the constraints of the available hardware resources. By incorporating optimization techniques including shared parallel computing units, hybrid-precision computing for a hybrid update mechanism, and the globally asynchronous and locally synchronous (GALS) strategy, we achieve a maximum network size of 150x10 and a peak working frequency of 100 MHz for the BCPNN-based associative memory system on the Xilinx Alveo U200 Card. The tradeoff between performance and hardware overhead of the design is explored and evaluated. Compared with the GPU counterpart, the FPGA-based implementation demonstrates significant improvements in both performance and energy efficiency, achieving a maximum latency reduction of 33.25x, and a power reduction of over 6.9x, all while maintaining the same network configuration.