The conditional directed acyclic graph (DAG) task model can represent the conditional execution flows that commonly exist in many real-time parallel applications. Previous work has shown that by properly assigning the priority among vertices inside a nonconditional DAG task, we can reduce the task response time and achieve better system schedulability. This article studies how to apply intra-task priority assignment to conditional DAG tasks. We develop a response time bound that theoretically dominates the state-of-the-art and present a novel algorithm to compute the bound in polynomial time. We further extend the proposed approach to the general setting of multiple conditional DAG tasks. Experiments with one conditional DAG task and multiple conditional DAG tasks demonstrate that our method consistently outperforms the state-of-the-art by a considerable margin.