This paper studies the higher order finite-time consensus protocol for heterogeneous multi-agent systems (HMASs). By adding a power integrator method and using heterogeneous domination method, two kinds of consensus protocols are proposed with state feedback and output feedback, respectively. First, for the leaderless and leader-follower HMASs, the continuous finite-time consensus protocols are proposed. Then, by designing a finite-time observer, the output-feedback finite-time consensus protocol is developed. Finally, simulations are performed to illustrate the effectiveness of the theoretical results.