The use of database management systems (DBMSs) as a cloud service is rapidly expanding. Cloud DBMSs offer many advantages, such as easier management, lower costs, and greater scalability. However, there are still security concerns regarding attacks from adversaries. DBMSs that use searchable encryption have been investigated with regard to ensuring their security. Because searchable encryption allows query execution over encrypted data in the cloud, sensitive data can be securely stored there in the cloud. On the other hand, encrypted query processing is slower than query processing on plaintext data. In this paper, we use a field-programmable gate array (FPGA) to accelerate query processing in a searchable encrypted DBMS. We also propose a new cache function to shorten the access time to database tables in a DBMS. According to an evaluation using basic queries, the proposed system has achieved up to 110.7 times speed-up compared with central processing unit (CPU) processing of a single core. In addition, the proposed system can process queries faster than the plaintext processing on a CPU when processing large amounts of data.