Recently, fault-tolerance control (FTC) methods have been proposed to further improve the reliability of T-type three-level converters. However, the application of model predictive control (MPC) in FTCs is rare, and the neutral point (NP) voltage imbalance before an open-switch fault occurs has not been solved. This article focuses on these two problems and proposes two FTC control methods: sequential MPC and sequential model predictive tolerance control. Both methods are implemented by designing a sequential predictive control that first considers the NP voltage balance and then grid current tracking. Through the staggered operation of the two methods, a T-type grid-connected converter with an LCL filter can operate normally after an open-switch fault occurs. Moreover, both methods can achieve the NP voltage balance and excellent grid current outputs, eliminate the time-consuming selection of weighting factors, and reduce the number of calculation loops compared with the traditional model predictive tolerance control, thereby improving the control flexibility. The performance and comparison of the open-switch FTC with respect to the NP voltage oscillations, total harmonic distortion of the grid current, and pole voltage were demonstrated using numerous simulation and experimental results.