Nowadays general-purpose computing on graphics processing units (GPGPUs) performs computations what were formerly handled by the CPU using hundreds of cores on GPUs. It often improves the performance of sequential computation when the running program is well-structured and formulated for massive threading. The CYK algorithm is a well-known algorithm for the context-free language membership test and has been used in many applications including grammar inferences, compilers and natural language processing. We revisit the CYK algorithm and its structural properties suitable for parallelization. Based on the discovered properties, we then parallelize the algorithm using different combinations of memory types and data allocation schemes using a GPU. We evaluate the algorithm based on real-world data and herein demonstrate the performance improvement compared with CPU-based computations.