Propagation properties of Airy-Gaussian beams in a biased photovoltaic-photorefractive crystal are numerically investigated by using split-step Fourier method. The results show that breathing solitons that propagate stablely along a straight line can be generated when the initial amplitude of the input Airy-Gaussian beams and the external bias field of the crystal are in certain ranges. The peak intensity and the breathing period of the soliton can be controlled by adjusting the initial amplitude and the external bias field. With the increase of the initial light field distribution factor, the mean peak intensity of the soliton firstly increases and then decreases, whereas the breathing period firstly decreases and then increases. With the increase of the beam decay coefficient, the mean peak intensity of the soliton firstly increases, then decreases, and increases again. In addition, the propagation direction of the soliton can tilt to the left with a negative launch angle and to the right with a positive launch angle. The launch angle only affects the output position of the soliton and has no influence on the intensity, width and breathing period of the soliton.