Benefiting from tens of GHz bandwidth, terahertz (THz) communication is considered to be a promising technology to provide ultra-high speed data rates for future 6G wireless systems. To compensate for the serious propagation attenuation of THz signals, massive multiple-input multiple-output (MIMO) with hybrid precoding can be utilized to generate directional beams with high array gains. However, the standard hybrid precoding architecture based on frequency-independent phase-shifters cannot cope with the beam split effect in THz massive MIMO systems, where the directional beams will split into different physical directions at different subcarrier frequencies. The beam split effect will result in a serious array gain loss across the entire bandwidth, which has not been well investigated in THz massive MIMO systems. In this paper, we first reveal and quantify the seriousness of the beam split effect in THz massive MIMO systems by analyzing the array gain loss it causes. Then, we propose a new precoding architecture called delay-phase precoding (DPP) to mitigate this effect. Specifically, the proposed DPP introduces a time delay network as a new precoding layer between radio-frequency chains and phase-shifters in the standard hybrid precoding architecture. In this way, conventional phase-controlled analog beamforming can be converted into delay-phase controlled analog beamforming. Unlike frequency-independent phase shifts, the time delay network introduced in the DPP can realize frequency-dependent phase shifts, which can be designed to generate frequency-dependent beams towards the target physical direction across the entire THz bandwidth. Due to the joint control of delay and phase, the proposed DPP can significantly relieve the array gain loss caused by the beam split effect. Furthermore, we propose a hardware structure by using true-time-delayers to realize the concept of DPP.