Multi-path effect makes high speed broadband communications a very challenging task due to the severe inter-symbol interference (ISI). By concentrating energy in both spatial and temporal domains, time-reversal (TR) transmission technique provides a great potential of low-complexity energy-efficient communications. In this paper, we develop a new concept of time-reversal division multiple access (TRDMA) as a wireless channel access method based on its high-resolution spatial focusing effect. We propose to use TR structure in a multi-user downlink system over large delay spread channels, where the signals of different users are separated solely by TRDMA. Both the single-transmit-antenna scheme and its enhanced version with multiple-transmit-antenna are developed and evaluated in this paper. We investigate the system performance in terms of the effective SINR and the achievable sum rate of the multi-user system. It is shown in both analytical and simulation results that satisfying performances can be achieved in the proposed TRDMA multi-user downlink system.