The problem of state estimation for Markovian jumping Hopfield neural networks (MJHNNs) with delays is addressed in this paper. It is assumed that sector- bounded conditions are obeyed by the neuron activation function and perturbed function of the measurement equation. An LMI (linear matrix inequality) based state estimator and a stability criterion for delay MJHNNs are developed. It is shown that the designed estimator ensures the mean-square exponential stability of the resulting error system. Moreover, the delay-dependent sufficient conditions are derived in a simple and effective manner. Numerical results are presented which show that the proposed method is very promising for state estimation of Hopfield neural networks.