We propose a spatial diffuseness feature for deep neural network (DNN)-based automatic speech recognition to improve recognition accuracy in reverberant and noisy environments. The feature is computed in real-time from multiple microphone signals without requiring knowledge or estimation of the direction of arrival, and represents the relative amount of diffuse noise in each time and frequency bin. It is shown that using the diffuseness feature as an additional input to a DNN-based acoustic model leads to a reduced word error rate for the REVERB challenge corpus, both compared to logmelspec features extracted from noisy signals, and features enhanced by spectral subtraction.