In this study, we theoretically and experimentally demonstrate that the convolutional neural network (CNN) in combination with the residual blocks and the regression methods can be used to precisely and quickly reconstruct the OAM spectrum of a hybrid OAM mode no matter how the consistent OAM modes have the same or different order indices in both the azimuthal and the radial direction. For cases of the simulation testing, the mean errors of all recognized parameters for hybrid OAM modes in a four-mode fiber (4MF) and a six-mode fiber (6MF) are smaller than 0.003 and 0.008, respectively. To the best of our knowledge, this is the first time that all the OAM modes, probably existing in the core of 4MFs or 6MFs, can be precisely and quickly recognized from intensity distribution of the hybrid OAM mode itself via the deep learning method.