Edge computing can realize a data locality among a cloud and users, and it can be applied to task offloading, i.e., a part of workload on a mobile terminal is moved to an edge or a cloud system to minimize the response time with reducing energy consumption. Mobile workflow jobs have been widely used due to advance of computational power on a mobile terminal. Thus, how to offload or schedule each task in a mobile workflow is one of the current challenging issues. In this paper, we propose a task scheduling algorithm with task offloading, called priority-based continuous task selection for offloading (PCTSO), to minimize the schedule length with energy consumption at a mobile client being reduced. PCTSO tries to select dependent tasks such that many tasks are offloaded so as to utilize many vCPUs in the edge cloud; in this manner, the degree of parallelism can be maintained. Experimental results of the simulation demonstration that PCTSO outperforms other algorithms in the schedule length and satisfies the energy constraint.