Aiming at the scenarios that the query issuers and query sender are uncertain moving objects, a new type of queries named DRqTI (Distance-based Range query within a Time Interval) is defined. The DRqTI searches out the target object in the dataset, which satisfies that the distance to the query issuer does not exceed the threshold value in a given time interval. And query results contain the suitability and valid time intervals which satisfy the condition. Three pruning strategies, namely trajectory-based, time-based and distance-based rules are designed. Furthermore, algorithms that integrate the calculation method of refining and matching degree are developed. On this basis, a query processing algorithm is designed. The experimental analysis shows that distance-based method is the best among three methods and the proposed algorithm can deal with DRqTI problem efficiently.