This paper introduces a fault-tolerant consensus control approach for a continuous multi-agent system with actuator faults. The faults in the multi-agent system are modelled as additive and multi- plicative actuator faults. The objective is to design a leader-following control for consensus-based Linear Parameter Varying (LPV) multi-agent systems. The proposed control approach employs a leader-following strategy, where the dynamics of the LPV virtual leader are defined. The synchro-nisation error between the followers and the virtual leader is considered, and a consensus control law is introduced. The fault-tolerant mechanism involves the design of a distributed LPV observer and an LPV virtual actuator. Fault-tolerance is achieved through the redistribution of control inputs based on the effectiveness of actuators and dynamic virtual actuators. The primary focus is on establishing Linear Matrix Inequalities (LMIs) conditions ensuring the existence of LPV consensus control, LPV observers, and LPV virtual actuator gains. To demonstrate the effectiveness of the proposed fault-tolerant control, simulation results considering a team of Unmanned Aerial Vehicles (UAVs) in formation under actuator faults are presented.