Exploiting low precision computing in scientific computations is now one of attractive research issues. Under this background, we aim for developing mixed precision linear solvers in which 1) low precision computing can be exploited, and 2) the accuracy of the final solution can be retained compared with conventional solvers using only standard precision (e.g., FP64). Such solvers will be expected to be easily used in various applications. In this talk, we present our recent attempt to introducing low precision computing into the GMRES(m) method, which has been widely used for solving a system of linear equations with a large, sparse, and general (non-symmetric) coefficient matrix. Based on the structure of the iterative refinement included in GMRES(m), we reasonably introduce low precision computing into GMRES(m). Then, for various precision settings, we experimentally investigate the numerical behaviors of the mixed precision GMRES(m). The obtained numerical results indicate the potential of aggressively exploiting low precision computing in GMRES(m). This is joint work with Takeshi Iwashita and Yingqi Zhao, Hokkaido University.