With the rapid development of medical information systems, the information system based on medical clouds stores massive electronic health records (EHRs) in medical cloud systems and employs the powerful storage and computing capacity of medical clouds to manage EHRs in a safe and unified manner. Although the traditional encryption mechanism can protect the privacy of medical data in semi-honest cloud servers, it is still an open problem to perform safe and efficient range-based search for the encrypted EHRs. To address this problem, in this work, a range-based multi-keyword searchable scheme is proposed. It can implement searchable encryption of complex query structures with scalar-product preserving encryption and support the query of connection keywords, ranges, and wildcard characters. Furthermore, the indexes and trapdoors are created in a random manner to hide the search mode and protect the privacy of search statements. The Hadamard product is adopted to reduce the dimension of the required key matrix. Theoretical analysis and experimental results show that the scheme can efficiently protect the privacy users' search strategy while guaranteeing the privacy of medical data. This scheme improves the retrieval efficiency and reduces the time in index and trapdoor creation, achieving the range-based search of medical data in multi-user and multi-file medical environments.