All-optical diodes and all-optical transistors are the basis of all-optical logic devices. We study the quantum statistical properties of all-optical diodes based on cavity quantum electrodynamics (QED) ^{[ 1 ]}, and discuss the squeezed properties of the output light after passing through the diode when coherent light and squeezed light are incident. Here we extend our research to all-optical transistor, and take all-optical transistor based on cavity optomechanical system as the research object. By changing the intensity of classical pump light, the all-optical transistor can effectively control the output of the probe light and realize optical amplification. We discuss the squeezed properties of the output light of the all-optical transistor with squeezed light and coherent light as the probe light. Our results show that when the probe light is coherent, the output light remains coherent no matter whether it works in the amplified region, and is not squeezed. When the input probe light is amplitude squeezed light, the output light is still squeezed light in the light amplification region of all-optical transistor, but the squeezed properties are modulated by the input light squeezed properties and system parameters. When the squeezed angle of the input probe squeezed light is 0°, the minimum squeezed parameter S ₁of the output squeezed light decreases with the increase of the squeezed coefficient r of the input probe light, and the minimum value approaches to the squeezed limit of –0.25. But the change of squeezed angle of the input probe squeezed light changes has a great influence on the squeezed parameter S _1,2of the output light, and the squeezed properties will disappear. Only when the squeezed angle is an integer multiple of π, will the squeezed properties of the output light be best. This result has a potential application value in quantum measurement, weak signal detection, and other fields.