The terahertz communication system with traditional hybrid precoding structure has the problem of beam diffusion. This problem leads to the serious loss of achievable rate and offsets the performance gain caused by bandwidth increase, so a broadband hybrid precoding scheme based on cyclic delay is proposed in this paper. Firstly, a broadband hybrid precoding framework based on cyclic delay is constructed. A delay element is placed at each antenna of the traditional full-connected hybrid precoding structure. Thus, a frequency-dependent phase shift is accomplished to compensate the beam diffusion. Then, the unit delay of delay element at each antenna is determined by maximizing the array gain of the sub-carriers, but there is a problem that the unit delay is not uniform. Finally, through the design of analog precoding, the unity of the unit delay can be realized, while maximizing the array gain of each sub-carrier. The simulation results show that the proposed scheme can achieve 100% array gain at any sub-carrier, and is suitable for solving the problem of beam diffusion under different bandwidth and different number of transmit antennas. Compared with the existing schemes, the achievable rate of the proposed scheme is very close to that of the full-digital precoding scheme, and has the advantage of high energy efficiency.