In recent years, distributed scientific workflows structured as directed acyclic graph (DAG) are widely applied to various research areas to enable science discovery. In a heterogeneous distributed computing environment, computing nodes and communication link failures are inevitable and could have an negative impact on the applications. Efficient mapping and scheduling algorithms to achieve both the low end-to-end delay and the high reliability have been attracting active research interests. However, it is not possible to optimize both objectives due to conflicting requirements. We proposed a mapping and scheduling algorithm, namely Fault-tolerant Workflow Mapping Algorithm under End-to-end Delay Constraint (FMEDC), which considers both the execution delay and reliability in a two-step procedure. In the first step, a hybrid mapping algorithm combining recursive critical path searching and layer-based priority techniques (HCPT) is developed to achieve the minimum end-to-end delay(MED) along the critical path. The computation and communication failure rates are factored into equation to compute the reliability-enhanced execution time. In the second step, the modules on the non-critical paths are rescheduled onto nodes in a way such that system reliability can be improved under the MED constraint calculated in the first step. Experimental results show that our algorithm achieves the lowest MED but highest reliability under the same time constraints compared with some representative algorithms.