In this paper, considering the input saturation, off-diagonal mass matrix, model uncertainties and time-varying environment disturbances, an adaptive neural path following control strategy, which is based on the surge-heading line-of-sight guidance law, is presented for underactuated surface vessels. In view of the practical situation, we consider that the mass and damping matrices are off-diagonal. For the sake of better path following performance, a surge-heading line-of-sight guidance law is established, where the surge-heading line-of-sight guidance law not only generates the desired heading angle, but also designs the desired surge speed for the control system. Then, adaptive neural path following controllers are designed to track the referenced signals, where the input saturation nonlinearity is handled by a hyperbolic tangent function, and the lumped disturbances including external environment disturbances, approximation errors and model uncertainties are approximated by adaptive radial basis function neural network. On the basis of the proposed control scheme, all error signals of the whole system are proven to be uniformly ultimately bounded, so that the target of path following problem is realized. At last, simulation results are applied to indicate that the presented approach is effective. INDEX TERMS Input saturation, neural networks, path following, surge-heading line-of-sight.