A theoretical model of high power multimode fiber amplifier is built based on rate equations of the multimode rare earth doped fiber considering the launching condition of the seed light and improvement of the mode coupling in the core. The theoretical study on the effect of rare earth dopant profiles in the core on the output characteristics is carried out. The output characteristics of the high power multimode fiber amplifier with flat and parabolic dopant profiles fibers in different launching conditions are described respectively. The results indicate that the different rare earth dopant profiles may have different impacts on the output characteristics. Besides, the high order modes in the large core fiber can be suppressed and the output beam quality can be improved by designing and controlling the rare earth dopant profiles.