The accelerator system of the International Fusion Materials Irradiation Facility (IFMIF) provides the 250-mA, 40-MeV continuous-wave deuteron beam at one of the two lithium target stations. It consists of two identical linear accelerator modules, each of which independently delivers a 125-mA beam to the common footprint of 20 cm × 5 cm at the target surface. The accelerator module consists of an ion injector, a 175 MHz RFQ and eight DTL tanks, and rf power supply system. The requirements for the accelerator system and the design concept are described. The interface issues and operational considerations to attain the proposed availability are also discussed.