The methods based on traditional pattern recognition and deep learning have been successfully applied in gearbox intelligent diagnosis. However, traditional pattern recognition methods cannot directly classify feature tensors of multi-source signals, and deep learning networks hardly handle the classification of small samples. Therefore, for the gearbox intelligent diagnosis with multi-source signals, a novel tensor classifier called kernel flexible and displaceable convex hull based tensor machine (KFDCH-TM) is proposed. In KFDCH-TM, the kernel flexible and displaceable convex hull of tensor samples in tensor feature space is defined firstly. Then, an optimal separating hyper-plane between two kernel flexible and displaceable convex hulls is constructed. Meanwhile, feature tensors extracted from multi-source signals through wavelet packet transform (WPT) are used to diagnose gearbox fault by KFDCH-TM. The results of two cases demonstrate that KFDCH-TM can effectively identify gearbox fault with multi-source signals and has better robustness.