A fuel injection rate control apparatus for a V-engine, formed so that the rational speed of the engine can be prevented from varying when the engine is inclined forward or backward, even if a commonly mass-produced inexpensive governer is used. This control apparatus has a fuel injection pump (1) provided with a governer (2) and mounted on one side portion of a cylinder block, a governer-free fuel injection pump (1') mounted on the other side portion of the cylinder block, and a link mechanism consisting of a connecting shaft (4.sub.1) provided in front of the two fuel injection pumps so that the connecting shaft can be turned freely so as to transmit the movement of a rack rod (3) of the governer-carrying fuel injection pump (1) to a rack rod (3) of the other fuel injection pump (1'), a pair of levers (4.sub.2-1, 4.sub.2-2) fixed to both sides of the connecting shaft so as to project in the opposite directions, and a pair of links (4.sub.3) connecting these levers and two rack rods together.