This paper proposes a novel method to schedule parallel execution of planning and action. The method is for a class of planning problems which are hierarchically decomposed into two subproblems: (1) determining the next subgoal and (2) determining and executing an action sequence to achieve the subgoal. In this problem class, the upper-level planning process can be viewed as a process of gradually reducing the subgoal candidates towards the final commitment to one subgoal. Using criteria on deciding if a ground-level action sequence is consistent with the remaining subgoal candidates (consistency criterion), and on when to commit to one subgoal (commitment criterion), appropriate action sequence is selected and executed while the upper-level planning process is still continuing. Preliminary experimental results including the comparison with a sequential method show that the proposed method is promising.