Recently, the use of low precision computing (e.g., FP32 and Fp16) in scientific computations has attracted attentions in the HPC community. Under this situation, for solving a system of liner equations with a large and sparse coefficient matrix, we have developed a numerical method that uses low precision computing. We aim for developing methods that can exploit low precision computing and retain the accuracy of the final solution compare d with conventional methods using only standard precision (e.g., FP64). In our current study, where we focus on the GMRES(m) method, the mixed precision version of the GMRES(m) method has been designed, and we have conducted several numerical experiments to investigate the possibility of introducing low precision computing into the GMRES(m) method. In this talk, we present our experimental results that indicate the potential of the mixed precision GMRES(m) method using low precision computing. This is joint work with Takeshi Iwashita and Yingqi Zhao, Hokkaido University.