Processing latency is a critical issue for active noise control (ANC) due to the causality constraint of ANC systems. This paper addresses low-latency ANC in the deep learning framework (i.e. deep ANC). A time-domain method using an attentive recurrent network is employed to perform deep ANC with smaller frame sizes, thus reducing algorithmic latency of deep ANC. In addition, a delay-compensated training strategy is introduced to perform ANC using predicted noise for several milliseconds. Moreover, we utilize a revised overlap-add method during signal resynthesis to avoid the latency introduced due to overlaps between neighboring time frames. Experimental results show that the proposed strategies are effective for achieving low-latency deep ANC. Combining the proposed strategies is capable of yielding zero, even negative, algorithmic latency without significantly affecting ANC performance.