We report the characteristics of a diode-end-pumped, high-repetition-rate, acoustic-optic (AO) Q-switched Tm:YLF laser operating from 5 kHz to 10 kHz. In the continuous-wave (CW) regime, a maximum average output power of 8.5 W was obtained with a slope efficiency of 30.7%. Under the AO Q-switching regime, a maximum output power of 7.32 W was obtained at a repetition frequency of 5 kHz with a pulse width of 68 ns and a pulse energy of 1.4 mJ, corresponding to a peak power of 21.5 kW. A time-dependent rate equation model is introduced to theoretically analyze the results obtained in the experiment, in which the cross-relaxation phenomenon, upconversion losses and ground-state depletion are taken into account. Additionally, the evolution processes of population inversion density and intracavity photon number density with time are also presented. The theoretical results well predict the dependence of laser output characteristics of Tm:YLF crystal on the incident pump powers.