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In this paper, the adaptive fault-tolerant control (FTC) problem of heterogeneous multi-agent systems (HMASs) with state constraints composed of first-order and second-order agents is studied. The problems of fault and constraints are inevitable during the operation of the system, the authors consider the fault of the system as actuator fault, and the constraints of the system can be considered as state constraints. Based on the backstepping framework, the logarithmic barrier Lyapunov function is selected to study the stability of system with constraints. For the bias fault of actuator fault, adaptive estimation is carried out, which can estimate the fault more accurately. Finally, an adaptive constrained FTC scheme is successfully designed to ensure that each signal of the system is bounded. Simulation examples show that the constrained FTC scheme is effective.