With the increase in transmission rate and transmission distance, the impact of nonlinear impairments on the performance of long-haul fiber-optic communication systems becomes increasingly significant, severely restricting overall system performance. In order to mitigate integrated effects of nonlinear impairment for the long-haul fiber-optic communication system, a dual-branch hybrid neural network-based nonlinear impairment compensation method for the long-haul optical communication system is proposed. Firstly, the channel memory is leveraged by the model to capture the global feature of channel impairments in the time domain, so as to optimize feature learning of current symbols through historical information; Secondly, the spatial features of symbols in the constellation diagram are captured by the real-valued branch based on convolutional neural networks, and the channel attention mechanism and the spatial attention mechanism are adopted to enhance the learning capability of the model for nonlinear impairment-related spatial features; Finally, the latent information of phase and amplitude variations of complex symbols is captured by the complex-valued branch, thereby the combined effects of nonlinear impairments are effectively compensated. Numerical simulation is established with self-phase modulation and cross-phase modulation as the primary nonlinear effects, simulation results demonstrate that the proposed method achieves a lower bit error rate and exhibits stability under varying conditions of transmitted optical power, transmission distance and symbol rate.