This paper presents a reliable variable pitch propeller (VPP) quadcopter with a cambered airfoil propeller called Heli-quad that achieves full-attitude control under a complete failure of one actuator. The idea of employing a cambered airfoil in the propeller blade plays a pivotal role in the full attitude control under the failure of an actuator. Experimental data shows that the cambered airfoil propellers generate significantly higher torque than symmetric airfoil propellers, enabling yaw control even under a complete failure of an actuator. The theoretical analysis clearly indicates that Heli-Quad with three actuators is sufficient to provide full-attitude control. The proposed unified fault-tolerant controller consists of a outer loop position tracking controller, a proportional-derivative inner loop attitude controller, and a novel neural-network-based reconfigurable control allocation scheme that computes the actuator commands. Experimentally validated propeller aerodynamic data has been used to train the neural network. High-fidelity software-in-the-loop simulations using the SIMSCAPE environment are carried out to analyze the Heli-quad’s performance. From the empirical result, the maximum tolerable delay in Fault Detection and Isolation (FDI) is 180 ms. The results indicate that even under the complete failure of one actuator, the position tracking performance of the Heli-quad is closer to nominal conditions.