This paper addresses the time-varying formation control problem of second-order networked multi-agent systems consisting of a virtual leader and multiple followers, where random communication constraints in the forward and feedback channels as well as actuator and sensor faults are considered. A state observer is designed to estimate the system state and the potential faults, based on which a time-varying formation active fault-tolerant predictive control scheme is proposed. Then, a necessary and sufficient condition is derived to guarantee the stability of the closed-loop system and to achieve the time-varying formation, which is independent of random communication constraints as well as actuator and sensor faults. Finally, simulation results of three contrastive cases are presented to verify the effectiveness of the proposed control scheme.