The invention discloses a cantilever formwork for concrete construction and a construction method thereof, and belongs to the technical field of bridge construction. The problems that construction iscomplicated, cost is high and concrete surface smoothness is low when the outer surfaces of all supporting columns of a bridge are constructed are solved. The cantilever formwork comprises a cantilever formwork support, an anchoring assembly and a planar formwork and is a single-sided wall body climbing formwork used for formwork construction of concrete linings and other structures of dams, piers, concrete retaining walls, tunnels and underground plants, the formwork is easy and rapid to construct and economical, the concrete surface is smooth, the support, the formwork and construction loadsare all borne by an embedded piece assembly, no scaffold needs to be additionally erected, and the formwork is suitable for aloft operation; by means of an anchoring device, the formwork is closely attached to a concrete wall surface, and mortar leakage and slab end faulting are prevented; an inclined strut is arranged on the cantilever support, and the perpendicularity of the formwork can be conveniently adjusted; all connectors are standard, universality is high, and a hanging platform is arranged at the lower portion of the formwork and can be used for assembling and disassembling embeddedpieces and processing the concrete surface.