The difficulty of solving nonlinear equation systems (NESs) lies in how to achieve the synchronous parsing of multiple-root joint solution. Since neighborhood-based crowding differential evolution algorithm has many problems such as incomplete solution of multiple roots, loss of roots and easy to fall into local optimality, a neighborhood crossover-based dual-mutation differential evolution algorithm is proposed. The dual-mutation strategy is based on individual fitness values to learn both neighborhood and global evolutionary information, which results in improving population diversity and simultaneously enhancing the local optimum avoidance performance. The neighborhood crossover strategy employs the population grouping mechanism and different crossover operations to achieve differential guidance of evolutionary individuals, which contributes to avoiding the loss of joint solution of multiple roots and improving the computing resources utilization efficiency. The experimental results show that the proposed algorithm can effectively realize the multi-root joint solution of NESs and has outstanding capacity on the index of root rate and success rate.