In this paper, an adaptive neural network learning based nonsynchronous control method is developed for hidden Markov jump systems with unmodeled nonlinear dynamics. In particular, the system modes are not directly accessible and the limited mode information can be partly estimated by the nonsynchronous controller. More precisely, the mode information with partly accessible transition rates is utilized based on the transition probability matrix. Moreover, the unmodeled nonlinear dynamics are more general in practical applications. Based on the designed mode-dependent controllers with mode observation, sufficient conditions are first exploited by means of the Lyapunov method, such that the desired control performance could be ensured in the mean-square sense. Then, the nonsynchronous mode-dependent controllers are further determined in terms of convex optimization. In the end, our proposed control strategy is applied to a robotic manipulator with varying loads to validate the feasibility with simulation results.