It is highly desirable that speech enhancement algorithms can achieve good performance while keeping low latency for many applications, such as digital hearing aids, acoustically transparent hearing devices, and public address systems. To improve the performance of traditional low-latency speech enhancement algorithms, a deep filter-bank equalizer (FBE) framework was proposed, which integrated a deep learning-based subband noise reduction network with a deep learning-based shortened digital filter mapping network. In the first network, a deep learning model was trained with a controllable small frame shift to satisfy the low-latency demand, i.e., $\le$ 4 ms, so as to obtain (complex) subband gains, which could be regarded as an adaptive digital filter in each frame. In the second network, to reduce the latency, this adaptive digital filter was implicitly shortened by a deep learning-based framework, and was then applied to noisy speech to reconstruct the enhanced speech without the overlap-add method. Experimental results on the WSJ0-SI84 corpus indicated that the proposed deep FBE with only 4-ms latency achieved much better performance than traditional low-latency speech enhancement algorithms in terms of the indices such as PESQ, STOI, and the amount of noise reduction.