The robustness of the Kalman filter to double talk and its rapid convergence make it a popular approach for addressing acoustic echo cancellation (AEC) challenges. However, the inability to model nonlinearity and the need to tune control parameters cast limitations on such adaptive filtering algorithms. In this paper, we integrate the frequency domain Kalman filter (FDKF) and deep neural networks (DNNs) into a hybrid method, called NeuralKalman, to leverage the advantages of deep learning and adaptive filtering algorithms. Specifically, we employ a DNN to estimate nonlinearly distorted far-end signals, a transition factor, and the nonlinear transition function in the state equation of the FDKF algorithm. Experimental results show that the proposed NeuralKalman improves the performance of FDKF significantly and outperforms strong baseline methods.