The third-generation DNA sequencing technologies, such as Nanopore Sequencing, can operate at very high speeds and produce longer reads, which in turn results in a challenge for the computational analysis of such massive data. Nanopolish is a software package for signal-level analysis of Oxford Nanopore sequencing data. Call-methylation module of Nanopolish can detect methylation based on Hidden Markov Model (HMM). However, Nanopolish is limited by the long running time of some serial and computationally-expensive processes. Among these, Adaptive Banded Event Alignment (ABEA) is the most time-consuming step, and the prior work, f5c, has already parallelized and optimized ABEA on GPU. As a result, the remaining methylation score calculation part, which uses HMM to identify if a given base is methylated or not, has become the new performance bottleneck. This paper focuses on the call-methylation module that resides in the Nanopolish package. We propose Galaxy-methyl, which parallelizes and optimizes the methylation score calculation step on GPU and then pipelines the four steps of the call-methylation module. Galaxy-methyl increases the execution concurrency across CPUs and GPUs as well as hardware resource utilization for both. The experimental results collected indicate that Galaxy-methyl can achieve 3x-5x speedup compared to Nanopolish, and reduce the total execution time by 35% compared to f5c, on average. The source code of Galaxy-methyl is available at https://github.com/fengyilin118/.