In path planning, the influence of positionability on path planning should be considered in order to make the robot have highprecision positioning ability. Based on the classical A* path planning algorithm, an improved A* path planning method was proposed,in which the localizability was considered in the process of searching the path. The Cramer-Luo lower bound was introduced to predict the upper bound of the positioning variance of any grid, and the upper bound of the variance was transformed into the entropy of positioning information to describe the localizability. A new cost function was designed, which incorporated localizability to comprehensively evaluate search directions. The results show that compared with the classical A* algorithm, the path obtained by the improved method can successfully avoid the poorly locatable regions, making the path planning result more practical.