The lens system forms an image conjugately between each of a magnification conjugate point and a reduction conjugate point; and an intermediate image-forming position. The lens system includes a magnification optical system with positive power, the magnification optical system having a plurality of lens elements and positioned closer to the magnification side than the intermediate image-forming position; and a relay optical system with positive power, the relay optical system having a plurality of lens elements and positioned closer to the reduction side than the intermediate image-forming position. The lens system satisfies following conditions (1) and (2). 0.08≤fp/fr≤0.8  (1) {Ymax−ft·tan(ωmax)}/{ft·tan(ωmax)}≤−0.3  (2) where fr is composite focal length of the relay optical system, fp is composite focal length of the magnification optical system, Ymax is a radius of an effective image diameter, ωmax is a maximum half view angle, and ft is the focal length of the lens system.