The main contribution of this paper is to present a workoptimal parallel algorithm for LZW decompression and to implement it in a CUDA-enabled GPU. Since sequential LZW decompression creates a dictionary table by reading codes in a compressed file one by one, it is not easy to parallelize it. We first present a work-optimal parallel LZW decompression algorithm on the CREW-PRAM (Concurrent-Read Exclusive-Write Parallel Random Access Machine), which is a standard theoretical parallel computing model with a shared memory. We then go on to present an efficient implementation of this parallel algorithm on a GPU. The experimental results show that our GPU implementation performs LZW decompression in 1.15 milliseconds for a gray scale TIFF image with 4096 x 3072 pixels stored in the global memory of GeForce GTX 980. On the other hand, sequential LZW decompression for the same image stored in the main memory of Intel Core i7 CPU takes 50.1 milliseconds. Thus, our parallel LZW decompression on the global memory of the GPU is 43.6 times faster than a sequential LZW decompression on the main memory of the CPU for this image. To show the applicability of our GPU implementation for LZW decompression, we evaluated the SSD-GPU data loading time for three scenarios. The experimental results show that the scenario using our LZW decompression on the GPU is faster than the others.