In this study, we propose a new nonlinear generalized predictive control method for a class of discrete-time single-input single-output nonlinear dynamic systems. For this, we combine nonlinear switching control and unmodeled dynamics estimation methods based on deep learning technology. In the new algorithm, we use long short-term memory neural networks to estimate the unknown increment of unmodeled dynamics based on deep learning technology. We then enhance control performance by designing a nonlinear generalized predictive controller with unmodeled dynamic increment estimation. We also analyze the stability and convergence of the proposed control algorithm. The results of our simulation experiments verified the effectiveness of the proposed method.