In order to study the influence of pump bandwidth and wavelength-drift on the performance of solid-state lasers, theoretical analyses were performed on a quasi-three-level Tm:YAG laser, and the corresponding theoretical models, including both spectral and thermal models, were presented. In the Tm laser experiment, a compact and high-efficiency composite Tm laser operating at 2 013.2 nm was demonstrated, which was end-pumped by volume Bragg gratings(VBGs) locked laser diode(LD) with emission wavelength centered at 784.9 nm and bandwidth as narrow as 0.1 nm(full width at the half maximum, FWHM). A maximum output power of 7.96 W was obtained with a slope efficiency of 62.5% and optical conversion efficiency of 53.3%, respectively. The maximum laser wavelength drifted from 2 013.25 nm to 2 014.53 nm when increasing the absorbed pump power from 1.87 W to 14.93 W for the 3% output coupling. As for 5% output coupling, the drift was from 2 013.91 nm to 2 014.26 nm. It was found that a narrow LD bandwidth of 0.1 nm resulted in a more pronounced excitation efficiency and thus a higher laser efficiency, despite that the maximum temperature within the crystal was slightly higher. The present study could be extended to other solid-state lasers for the choice of pump source by comprehensively considering the pump bandwidth and wavelength-drift and the spectral profiles of gain medium, which would be helpful for an efficient laser system.