A new method for calculating the beam radius distribution of the input Gaussian beam and the laser mode volume in the laser rod of a solid-state laser amplifier is reported. By this method, we investigate how the strong thermal lens effects in the rod of amplifier and the waist radius and mode of the laser beam inputting to the rod of amplifier influence the input laser beam distributions and input beam mode volume in the rod of amplifier. It is shows that the expanded and collimated laser beam inputting to the rod of amplifier will be strongly reflected to the axis of the rod by the strong thermal lens effects in the rod, because the small far-field divergence angle of the collimated input laser beam results in the signigicant decrease of the mode volume of input laser beam and the overlap efficiency of amplifier drops. It can obviously increase the mode volume of input laser beam in the rod of the amplifier to input the laser beam with larger angle, which can counteract the reflecting effects on the input laser beam. Moreover, the beam waist radius of the multi-mode laser beam inputting to the amplifier should be larger than that of the fundamental-mode input laser beam, since its far-field divergence angle is larger than that of the fundamental-mode laser beam with the same beam waist radius.