Based on the nonlinear fractional Schrdinger equation, the effects of nonlinear gain and linear loss on the propagation characteristics of Gaussian beams are numerically studied. The results show that: the gaussian beam quickly evolved into the breathing soliton and we can control breathing soliton transmission behavior by changing system parameters. The changes in Lévy index have a good control effect on the pulse width, amplitude and period of the breathing solion. A larger Lévy index makes the pulse width larger, the amplitude smaller, and the soliton period larger. When there is no linear loss, the nonlinear gain weakened the beam diffraction, the pulse width is smaller in the transmission process, the soliton period decreases and the amplitude increases faster. Constant linear loss enhanced the diffraction of breathing soliton, the soliton period increases faster along the transmission direction, and the amplitude decreases faster at the same time. Therefore, the peak intensity of breathing soliton at the maximum compression can be kept unchanged by selecting the constant linear loss and the nonlinear gain reasonably. Cosine linear loss coefficient τ0 makes the soliton period increase faster along the transmission distance, but the frequency parameter β of the cosine function makes the soliton period increase slower along the transmission distance. So we can obtain the breathing soliton stability transmission by adjusting two parameters of the cosine function. When the nonlinear gain is not zero, comprehensively adjust various parameters, and the breathing soliton can be transmitted more stably. Exponential linear loss make the breathing soliton skew to left and the peak intensity attenuates exponentially along the transmission direction. The coefficient τ0 is larger, the attenuation rate is larger and the soliton period increases faster. The index β make the soliton skew to left further and the soliton period change slower. However, the nonlinear gain cannot balance the effect of exponential linear loss on the breathing solitons to obtain stable transmission. The results not only prove the controllability of gaussian beam propagation in nonuniform nonlinear fractional Schrdinger equation, but also provide a theoretical reference for optical signal processing in nonlinear optics.