In an off-axis pumped laser, the off-axis thermal lens effect gives rise to the Hermite-Gaussian (HG) mode hopping. Namely, with the pump power increasing, the running laser turns from a single HG mode into mixed modes and then into the adjacent low-order HG mode. Our analysis shows that this is due to the decrease in the effective off-axis amount caused by the off-axis thermal lens-induced optic axis shift of the resonant cavity for off-axis pumping. The experimental results demonstrate that a higher-order mode has a lower pump power for mode hopping. Moreover, we can return the laser to the original HG mode by modifying the off-axis amount in practice. A larger adjustment is required as the pump power increases. We experimentally demonstrate pulsed outputs at a high peak power in sixteen HG modes, from mode HG_1,0 to mode HG_16,0. At a repetition rate of 10 kHz, a pulse width of 32 ns and a peak power of 4.1 kW are realized for the mode HG_1,0, and a pulse width of 79 ns and a peak power of 0.7 kW are realized for the mode HG_16,0.