In this paper, based on the potential-free Schrdinger equation, the dynamic solution describing the evolution of the Pearcey-Gaussian beam is obtained. It is found that each lobe of the Pearcey-Gaussian beam isaccelerated in the transverse direction, and the farther away from the main lobe, the greater the acceleration of these side lobes. Eventually, the side lobes and the main lobe reach the same position at the same time. When passing this position, the direction of acceleration changes, so they slow down in the transverse direction. The difference in acceleration of the lobes leads to the separation of the lobes and the invertion of the profile of the Pearcey-Gaussian beam. Thus a focusing and inverting behavior forms. According to the analytical result, the analytical expression governing the focusing distance of the Pearcey-Gaussian beam with a small truncation coefficient is given and verified by numerical simulation. Moreover, the effect of the truncation coefficient on the dynamic behavior of the Pearcey-Gaussian beam is studied numerically by means of a symmetrized split-step Fourier scheme. The results show that the focusing behavior of the Pearcey-Gaussian beam weakens with the increasing of the truncation coefficient. When the truncation coefficient is large, the focusing behavior of the Pearcey-Gaussian beam disappears completely and is replaced by the diffusion behavior. Finally, the dependences of the focusing distance and the peak power at the focusing position on the truncation coefficient are investigated in detail. The results show that with the increasing of the truncation coefficient, the focusing distance decreases gradually, while the peak power at the focusing position decreases rapidly. The results have an important application value for generating an optical beam with high peak power by adjusting the truncation coefficient.