One of the most important queries in spatio-temporal databases that aim at managing moving objects efficiently is the continuous K-nearest neighbor (CKNN) query. A CKNN query is to retrieve the K-nearest neighbors (KNNs) of a moving user at each time instant within a user-given time interval [t s , t e ]. In this paper, we investigate how to process a CKNN query efficiently. Different from the previous related works, our work relieves the past assumption, that an object moves with a fixed velocity, by allowing that the velocity of the object can vary within a known range. Due to the introduction of this uncertainty on the velocity of each object, processing a CKNN query becomes much more complicated. We will discuss the complications incurred by this uncertainty and propose a cost-effective P2 KNN algorithm to find the objects that could be the KNNs at each time instant within the given query time interval. Besides, a probability-based model is designed to quantify the possibility of each object being one of the KNNs. Comprehensive experiments demonstrate the efficiency and the effectiveness of the proposed approach.