In AI planning community, planning domains with derived predicates are very challenging to many planning system. Derived predicate is a new application of domain rules and domain knowledge acquisition. In this paper, we propose an approach to planning with derived predicates: defining activation sets of a derived predicate which are unrelated to any specific state and computing them in the preprocess phase through the instantiation rule-graph; replacing a derived predicate with one of its activation sets in relax-plan to extract action sequences. And we also implement the proposed approach in a new planner, called FF-DP, which shows good performance in our experiments.