The scheduling of real-time tasks with primary-backup based fault-tolerant requirements has been an important problem for several years. Most of the known scheduling schemes are non-adaptive in nature meaning that they do not adapt to the dynamics of faults and task’s parameters in the system. In this paper,we propose an adaptive faulttolerant scheduling scheme that has a mechanism to control the overlap interval between the primary and backup versions of tasks such that the overall performance of the system is improved. The overlap interval is determined based on the estimated primary fault probability and task’s soft laxity. We also propose a new performance index that integrates schedulability (S) and reliability (R) into a single metric, called SR index. To evaluate the proposed scheme, we have conducted analytical and simulation studies under different fault and deadline scenarios, and found that the proposed adaptive scheme adapts to system dynamics and offers better SR index than that of the non-adaptive schemes.