In existing spatial range query authenticating methods such as VR-tree and MR-tree, the transmission cost of the server to the client is high and the verification efficiency of the client is low because the Verification Object (VO) contains too much authentication information. To resolve these problems, a new index structure MGR-tree was proposed. First of all, by means of embedding a R-tree in each leaf node of Grid-tree, the size of VO decreased, and the efficiency of query and authentication was improved. In addition, an optimal index MHGR-tree which takes advantage of the property of Hilbert curve and a filter policy were proposed to accelerate the verification. Experimental results show that the proposed method has a better performance compared with MR-tree. In the best case, the verification object size and authentication time of MHGR are 63% and 19% of MR respectively.