The fluid model is proposed to investigate the gas breakdown driven by a short-pulse (such as a Gaussian pulse) high-power microwave at high pressures. However, the fluid model requires specification of the electron energy distribution function (EEDF); the common assumption of a Maxwellian EEDF can result in the inaccurate breakdown prediction when the electrons are not in equilibrium. We confirm that the influence of the incident pulse shape on the EEDF is tiny at high pressures by using the particle-in-cell Monte Carlo collision (PIC-MCC) model. As a result, the EEDF for a rectangular microwave pulse directly derived from the Boltzmann equation solver Bolsig+ is introduced into the fluid model for predicting the breakdown threshold of the non-rectangular pulse over a wide range of pressures, and the obtained results are very well matched with those of the PIC-MCC simulations. The time evolution of a non-rectangular pulse breakdown in gas, obtained by the fluid model with the EEDF from Bolsig+, is presented and analyzed at different pressures. In addition, the effect of the incident pulse shape on the gas breakdown is discussed.