The quest for precise measurements of the muon's anomalous magnetic moment, prompted by the observed discrepancy between theoretical and experimental results by other experiments worldwide, is the motivation of the upcoming muon g-2/EDM experiment at J-PARC. The precise reconstruction of the positron tracks from muon decays plays a vital role, which is currently accomplished by a Hough transformation technique. However, due to the track-finding bottleneck in the reconstruction pipeline, a 40-fold reduction in computational time is essential. We present here the overview and status of a GPU-based approach to address this problem. The basic idea is to leverage the capability of GPU (Graphics Processing Units) to optimize the track finding through parallel execution utilizing multiple GPU threads, allowing for significant acceleration in computation. Initial studies have shown encouraging results but also indicate additional refinements required for high pileup conditions.