In this paper, we present a novel deep neural network (DNN) assisted subband Kalman filtering system for speech enhancement. In the off-line phase, a DNN is trained to explore the relationships between the features of the noisy subband speech and the linear prediction coefficients of the clean ones, which are the key parameters in Kalman filtering. In the on-line phase, the input noisy speech is firstly decomposed into subbands, and then Kalman filtering is applied to each subband speech for denoising. The final enhanced speech is obtained by synthesizing the enhanced subband speeches. Experimental results show that our proposed system outperforms three Kalman filtering based methods in terms of both speech quality and intelligibility.