The H + CH3OH reaction, which plays an important role in combustion and the interstellar medium, presents a prototypical system with multi channels and tight transition states. However, no globally reliable potential energy surface (PES) has been available to date. Here we develop global analytical PESs for this system using the permutation-invariant polynomial neural network (PIP-NN) and the high-dimensional neural network (HD-NN) methods based on a large number of data points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-zeta basis set (UCCSD(T)-F12a/AVTZ). We demonstrate that both machine learning PESs are able to accurately describe all dynamically relevant reaction channels. At a collision energy of 20 kcal/mol, quasi-classical trajectory calculations reveal that the dominant channel is the hydrogen abstraction from the methyl site, yielding H-2 + CH2OH. The reaction of this major channel takes place mainly via the direct rebound mechanism. Both the vibrational and rotational states of the H-2 product are relatively cold, and large portions of the available energy are converted into the product translational motion.