In this paper, the problem of time-varying narrowband leaked Orthogonal Frequency Division multiplexing (OFDM) channel estimation is considered. The leakage effect results from practical constraints on communication systems: finite bandwidth and block length. These practical constraints effectively render a sparse channel into a non-sparse one. The inherent low-rank structure of the received signal, determined by the number of dominant paths of the channel, is exploited. The current work extends prior work on single carrier systems to OFDM; herein, it is also known that leaked OFDM channel is separable in delay and Doppler domains. A convex optimization approach, based on the atomic norm heuristic, is developed. Optimality and uniqueness of the proposed channel estimation method are shown. Simulation results show superiority over the classical l1 element-wise sparse method with an average 8 dB improvement.