A reusable booster of the first stage of a launch vehicle, comprising a body including tanks for oxidizer and fuel, a nose compartment with a dome, a between-tank section and an afterbody, a rocket engine installation, a straight all-moving wing with a unit for turning it and fixing in a position along the axis of the booster during the ascension step and in a position turned by 90° during return flight, horizontal and vertical fin assemblies, a triple-point support landing gear consisting of two main supports mounted on the booster body, and a front support positioned in the nose-compartment, aerodynamic control organs and units for jointing to the second stage of the launch vehicle, characterized in that it is provided with an air-feed jet engine installation, comprising two engines with air intakes mounted in the nose compartment, and a propellant system with the main propellant tanks in the wing, working and balancing tanks in the nose compartment, wherein a wing is mounted on an upper surface of the booster body in the area of the between-tank section, a horizontal fin and a vertical fin are mounted on the afterbody and are made respectively in the form of a stabilizer consisting of two all-moving consoles with a small negative V-shaped angle, and a fin with a yaw rudder, the engines of the air-feed jet installation are provided with gas-line extensions with exhaust nozzles extending beyond the bypasses of the external contours of the nose compartment and closed by aerodynamic domes, said exhaust nozzles are shifted from the surface of the booster body and their axes are deflected from the surface of the oxidizer tank, the dome of the nose compartment is made in the form of a portion of a sphere and has two inlet apertures for said air intakes, closed by one turning plug provided with a drive mounted in the nose compartment.