This letter proposes a novel time-asynchronous non-orthogonal multiple access (TA-NOMA) in downlink multicarrier systems. TA-NOMA applies an intentional time offset to control interference between multi-users and to improve spectral efficiency. We first propose a transceiver design for TA-NOMA, and analyze a novel type of interference caused by the intentional time offset. Based on the analysis, a singular value decomposition (SVD)-based pre-processing scheme is proposed. Numerical results show that the proposed TA-NOMA with pre-processing has a superior spectral efficiency compared with conventional power-domain NOMA. Another remarkable feature is that TA-NOMA does not require any user pairing.