As cloud computing is established on the massive cheap server clusters, it causes compute nodes' software and hardware to go wrong. Different computing nodes and communications links have different failure rate. For the parallel task scheduling problem that cloud users have requirements for deadlines and executing reliability, we put forward to generate all possible execution schemes of a parallel task on a cloud computing system. All the execution schemes are constructed into an execution scheme graph (ESG), in which a path from the start point to end point corresponds to an execution scheme of a parallel task. Based on ESG, we propose the maximum reliability execution scheme solving algorithm MRES that searches the execution schemes which have maximum reliability cost while meeting the parallel task's deadline requirement. The experimental results show that MRES algorithm can effectively improve the executing success rate.