Fuel-injection system

A fuel injection system, comprising:

• a first injection valve that includes a first valve body that opens/closes a first injection hole that injects a gas fuel and a first body in which a back pressure chamber is formed, the back pressure chamber making the pressure of the gas fuel act on the first valve body as a valve closing force;
• a second injection valve that includes a second valve body that opens/closes a second injection hole that injects the gas fuel, a second body in which a second passage is formed, the second passage making the gas fuel circulate to the second injection hole, and an electric actuator that makes a valve opening force act on the second valve body;
• a communication pipe that makes the second passage and the back pressure chamber communicate with each other;
• and
• a control unit that controls an energization state to the electric actuator and controls the operation of the second valve body, wherein
• according to a required injection amount, the control unit switches:
• a first injection control of opening the second valve body for a predetermined time or more so that the pressure of the back pressure chamber lowers to the pressure of opening the first valve body;
• and
• a second injection control of opening the second valve body for less than the predetermined time so that the pressure of the back pressure chamber does not lower to the pressure of opening the first valve body.