Coarse-Grained Reconfigurable Architecture (CGRA), especially the one with multiple parallelized Processing Element Arrays (PEA), possesses flexible programmability and high parallel computational efficiency, which relies upon an efficient memory architecture to deliver the corresponding computing power. Multi-PEA oriented CGRA allows for mapping various applications and thus demands a flexible memory to adapt to the ever-changing workloads, whose parallel access also requires an efficient multi-port memory. However, the existing memory designs for CGRA are hard to satisfy those requirements since conventional rigid memories fail to provide the desired flexibility due to fixed structure, and traditional multi-port designs are impractical due to large overhead. Therefore, this paper proposes a hardware/software (HW/SW) hybrid reconfigurable multi-port memory architecture (RMP-MEM) with an instructive analysis for the multi-PEA oriented CGRA. RMP-MEM supports adaptive memory partition and programmer-defined access modes to adapt the different features of memory accesses. Also, RMP-MEM achieves an efficient multi-port implementation by a partially shared mechanism. Furthermore, the microarchitecture of RMP-MEM is optimized multi-directionally, resulting in a significant performance gain. The experimental results indicate that RMP-MEM reduces the parallel access latency by 81.1% and exhibits 28.3% energy efficiency improvement compared to prior designs.