The state estimation issue for the discrete-time nonlinear systems with Markov delay is investigated in this paper, where the redundant communication channel is considered to ensure the reliability of transmission. Because the channel capacity is limited, the packet dropout conditions of the main channel and the redundant channel are described by the Bernoulli stochastic variables. In addition, a mode-dependent estimator is proposed based on the current state and the delayed state, simultaneously. Combining with the impulsive control strategy, the efficiency of estimator is improved. An augmented estimation error system is proposed to deal with the Markov delay in the nonlinear system, subsequently, a sufficient condition that ensures the asymptotic stability of the augmented error system is obtained by a constructed Lyapunov functional candidate and the gains of the impulsive estimator are derived. Finally, a numerical example of moving vehicle is utilized to illustrate the developed results.