The goal of single-channel source separation is to produce an accurate estimation of multiple sources given a mixture where these sources overlap. In this paper, we propose a new architecture to do this called the quasi-dual-path network (QDPN). The main difference to previous methods which mostly use the dual-path approach is to have the advantages of the dual-path approach like the short-term and long-term pattern recognition without the disadvantages of the dual-path approach like the doubling of the input size. Since the input size of the QDPN is considerably smaller than the input size of the dual-path approach, it enables us to turn up the hyperparameters for more accuracy. On the WSJ02-Mix benchmark, the QDPN achieves a scale-invariant signal-to-noise ratio of 23.6 dB and on the WHAMR! benchmark, the QDPN reaches a scale-invariant signal-to-noise ratio of 14.4 dB.