In this paper, quantum entanglement and quantum coherence in the XXZ Heisenberg spin chain with three-site interaction are investigated. We employ concurrence and relative entropy to measure quantum entanglement and quantum coherence. The influence of XZX+YZY three-site interaction, XZY-YZX three-site interaction, and magnetic field on the concurrence and the relative entropy vary with temperature are mainly studied. It is found that there is no sudden death phenomena in quantum coherence, and the temperature range of quantum coherence is larger than that of quantum entanglement. In addition, at absolute zero temperature, quantum coherence can characterize the quantum phase transition phenomena. In the ferromagnetic case, increasing XZX+YZY three-site interaction is the most effective way to reduce the attenuation rate and enlarge the temperature range of quantum coherence. Nevertheless, in the anti-ferromagnetic case, the cooperation effect of XZX+YZY and XZY-YZX three-site interaction can increase the maximum quantum coherence significantly and retard its decay rate at zero magnetic field. Additionally, in ferromagnetic and anti-ferromagnetic cases, when magnetic field B<0, the temperature range of quantum coherence is increased obviously, which is beneficial to preserve nonzero quantum coherence.