Non-orthogonal multiple access (NOMA) allows several users to multiplex in the power-domain to improve spectral efficiency. To further improve its performance, it is desirable to reduce inter-user interference (IUI). In this paper, we propose a downlink asynchronous NOMA (ANOMA) scheme applicable to frequency-selective channels. The proposed scheme introduces an intentional symbol offset between the multiplexed signals to reduce IUI, and it employs cyclic-prefixed single-carrier transmission with frequency-domain equalization (FDE) to reduce inter-symbol interference. We show that the mean square error for the FDE of the proposed ANOMA scheme is smaller than that of a conventional NOMA scheme. Simulation results show that the proposed ANOMA with appropriate power allocation achieves a better sum rate compared to the conventional NOMA.