A fault-tolerant gait of multi-legged robots with static walking is a gait which can maintain gait stability and continue its walking against an occurrence of a leg failure. This paper proposes fault-tolerant gait planning of a quadruped robot walking over a rough planar terrain. The considered fault is a locked joint failure, which prevents a joint of a leg from moving and makes it locked in a known position. In this Paper, two-phase discontinuous gaits are presented as a new fault-tolerant gait for quadruped robots suffering from a locked joint failure. By comparing with previously developed one-phase discontinuous gaits, it is shown that the proposed gait has great advantages in gait performance such as the stride length and terrain adaptability. Based on the two-phase discontinuous gait, quasi follow-the-leader(FTL) gaits are constructed which enable a quadruped robot to traverse two-dimensional rough terrain after an occurrence of a locked joint failure. During walking, two front legs undergo the foot adjustment procedure for avoiding stepping on forbidden areas. The Proposed wait planning is verified by using computer graphics simulations.