The invention provides an oblique-damping restraint system for main girders of a cable-stayed bridge. The oblique-damping restraint system consists of a group of obliquely arranged dampers, wherein one ends of the dampers are connected to the main girders of the cable-stayed bridge, and the other ends of the dampers are connected to the cable tower of the cable-stayed bridge; the dampers are symmetrically arranged on two sides of the cable tower along the longitudinal axis of the cable-stayed bridge; according to the obliquely arranged dampers, a horizontal plane is adopted as a datum plane, an included angle is formed between the arrangement axis of each damper and the longitudinal axis of each of the main girders, and damping restraint in the longitudinal bridge direction and damping restraint in the transverse bridge direction are simultaneously provided for the main girders. The fully new damping restraint system for main girders of the cable-stayed bridge, disclosed by the invention, is created through the integration of a technique of vibration damping and seismic resistance, a technique of vibration damping and wind resistance, a technique of two-way control, and a technique of limited limiting; the damping restraint system fills up the blank of the bridge vibration damping technique, and a new standard for the bridge vibration damping technique is provided; the bridge vibration is comprehensively controlled, and the safety, the durability and the economy of the bridge are guaranteed; the structure is simplified; an accessible condition, a detectable condition, a maintainable condition and a replaceable condition are good.