Massive multiple-input multiple-output (MIMO) is a key technology in next generation wireless communication. However, the increasing number of radio frequency (RF) chains results in higher cost and power consumption. Given that hundreds or even thousands of transmit antennas are equipped at the base station (BS), low resolution digital-to-analog converters (DACs) are preferred to reduce the power consumption on both DACs and power amplifiers (PAs). Currently, there have been some studies about the application of low-resolution DACs for single-carrier systems. For multi-carrier systems, this problem hasn’t been fully investigated. This paper aims to design a 1-bit downlink precoding algorithm for massive multi-user MIMO orthogonal frequency division multiplexing (OFDM) systems. A nonlinear precoding algorithm is proposed, which can address the non-convex optimization problem with discrete output constraint and guarantee convergence. Meanwhile, the proposed algorithm factors in the different path-losses experienced by different users. Furthermore, some approximation schemes can be applied to bring down the computational complexity of the proposed algorithm further. Simulation results illustrate that our algorithm performs the best among other nonlinear precoding methods in OFDM systems.