Gear transmission is widely used in mechanical equipment. In practice, if the gearbox is damaged, it not only affects the yield rate but also damages other parts of machines; thus, increases the cost and difficulty of maintenance. With the advancement of technology, the concept of unmanned factories has been proposed; an automatic diagnosis system for the health management of gearboxes becomes necessary. In this paper, a compound fault diagnosis system for the gearbox based on convolutional neural network (CNN) is developed. Specifically, three-axis vibration signals measured by accelerometers are used as the input of the one-dimensional CNN; the detection of the existence and type of the fault is directly output. In testing, the model achieved nearly 100% accuracy on the fault samples we captured. Experimental evidence also shows that the frequency-domain data can provide better diagnostic results than the time-domain data due to the stable characteristics in the frequency spectrum. For practical usage, we demonstrated a remote fault diagnosis system through a local area network on an embedded platform. Furthermore, optimization of convolution kernels was also investigated. When moderately reducing the number of convolution kernels, it does not affect the diagnostic accuracy but greatly reduces the training time of the model.