Process is long-lived, distributed, heterogeneous, and always evolutive to cope with unforeseen environment. In this paper, an approach for process instance evolution is proposed, which is a formal approach that focuses on ensuring the "goal-based behavior consistency" between the evolved process instance and the original instance in order to avoid ad-hoc change of process model. The goal is regarded as the criterion of behavior consistency, so evolved process instance needs to be analyzed in formal methods to ensure that it can still achieve its goals. Through specifying the semantics of process model and goals as Büchi automaton, whether an executing process instance can achieve its goals or not is decided.