The invention provides an anti-galloping device for a single-loop power transmission line. The power transmission line comprises a tower body, a tower head and a transmission conductor, wherein the tower body is vertically arranged; the tower head is transversely arranged at the upper end of the tower body; the transmission conductor is arranged on the tower head; the anti-galloping device comprises conductor anti-galloping mechanisms, an adjusting mechanism and composite insulator assemblies; the conductor anti-galloping mechanisms are connected with the transmission conductor; the adjusting mechanism is arranged on the ground; and the composite insulator assemblies are arranged between the conductor anti-galloping mechanisms and between the conductor anti-galloping mechanisms and the adjusting mechanism respectively. A stabilizing device provided by the invention can meet the anti-galloping requirements of a power grid of a conductor line with a relatively large span, and has the advantages of being good in anti-galloping property, low in production cost and convenient to install.