Interactive graph search leverages human intelligence to categorize target labels in a hierarchy, which are useful for image classification, product categorization, and database search. However, many existing studies of interactive graph search aim at identifying a single target optimally, and suffer from the limitations of asking too many questions and not being able to handle multiple targets. To address these two limitations, in this paper, we study a new problem of budget constrained interactive graph search for multiple targets called kBM-IGS-problem. Specifically, given a set of multiple targets T in a hierarchy, and two parameters k and b, the goal is to identify a k-sized set of selections S such that the closeness between selections S and targets T is as small as possible, by asking at most a budget of b questions. We theoretically analyze the updating rules and design a penalty function to capture the closeness between selections and targets. To tackle the kBM-IGS-problem, we develop a novel framework to ask questions using the best vertex with the largest expected gain, which makes a balanced trade-off between target probability and benefit gain. Based on the kBM-IGS framework, we first propose an efficient algorithm STBIS to handle the SingleTarget problem, which is a special case of kBM-IGS. Then, we propose a dynamic programming based method kBM-DP to tackle the MultipleTargets problem. To further improve efficiency, we propose two heuristic but efficient algorithms kBM-Topk and kBM-DP+. kBM-Topk develops a variant gain function and selects the top-k vertices independently. kBM-DP+ uses an upper bound of gains and prunes disqualified vertices to save computations. Experiments on large real-world datasets with ground-truth targets verify both the effectiveness and efficiency of our proposed algorithms.