This paper discusses a parallelized event reconstruction of the COMET Phase-I experiment. The experiment aims to discover charged lepton flavor violation by observing 104.97 MeV electrons from neutrinoless muon-to-electron conversion in muonic atoms. The event reconstruction of electrons with multiple helix turns is a challenging problem because hit-to-turn classification requires a high computation cost. The introduced algorithm finds an optimal seed of position and momentum for each turn partition by investigating the residual sum of squares based on distance-of-closest-approach (DCA) between hits and a track extrapolated from the seed. Hits with DCA less than a cutoff value are classified for the turn represented by the seed. The classification performance was optimized by tuning the cutoff value and refining the set of classified hits. The workload was parallelized over the seeds and the hits by defining two GPU kernels, which record track parameters extrapolated from the seeds and finds the DCAs of hits, respectively. A reasonable efficiency and momentum resolution was obtained for a wide momentum region which covers both signal and background electrons. The event reconstruction results from the CPU and GPU were identical to each other. The benchmarked GPUs had an order of magnitude of speedup over a CPU with 16 cores while the exact speed gains varied depending on their architectures.