We propose new hybrid precoding schemes for the downlink transmission in a multi-user millimeter wave (mmWave) system over frequency selective channels. In the system, the multi-antenna base station (BS) employs the fully-connected architecture and uses orthogonal frequency-division multiplexing (OFDM) to serve multiple mobile users. We first propose an alternating minimization (AM)-based hybrid precoding scheme by transforming the wideband hybrid precoding problem to a narrowband hybrid precoding problem. We then propose a beamforming-based hybrid precoding scheme by exploiting the correlation of subchannels to profoundly reduce the computational complexity. Numerical results are presented to demonstrate the advantages of our proposed schemes relative to two existing schemes, as well as to examine the impact of system parameters on the achieved performance.