A multi-level quantum dot thermal amplifier with heat leakage is proposed. Based on the theory of the Landauer formula, the electron flux, the heat flux, the heat-pumping rate and the coefficient of performance are derived. The three-dimensional projection graphs of the heat-pumping rate and the coefficient of performance versus the relative central energy levels are plotted. Moreover, the influence of the energy-level spacing, the number of energy levels, the total coupling strength, the asymmetry factor and the heat leakage coefficient on the optimal performance parameters is analyzed in detail. By choosing appropriate values of the system parameters, one can enhance the maximum heat-pumping rate and coefficient of performance.