Multi-user communication traditionally uses either code division multiple access (CDMA) or time-division multiple access schemes. The chirp signals resilience to multipath and the Doppler effect makes it suitable for underwater acoustic communication. This paper presents a binary phase-coded hyperbolic frequency-modulated (BPC-HFM) for multi-user underwater acoustic communication. The proposed scheme has the advantage of both linear frequency-modulated signal, which is immune to multipath and Doppler offset, while PN sequence is encoded in such a manner that a waveform possesses either a phase shift of 0 or 180 depending upon the code which results in a unique orthogonal waveform for every user. As a result, it helps to reduce multiple access interference; in addition, the time-reversal mirror technique is used to enhance the performance of the system in the high multipath environment due to the virtue of hydro-acoustic channel. Furthermore, it uses a relatively simple matched filter-based receiver. To substantiate the robustness of the proposed multi-user waveforms three types of hydro-acoustic channels using the different numbers of multiple users are chosen for simulation and the bit error rate (BER) of the system is calculated. Furthermore, the results are compared to binary phase-coded linear frequency-modulated signal and conventional Direct sequence spread spectrum CDMA.