A giant magnetoresistance (GMR) sensor with a Wheatstone bridge structure and an out-of-plane linear response was developed. The spin-valve structure consists of a synthetic antiferromagnetic [(Co/Pt)n/Ru/(Pt/Co)n] reference layer with perpendicular magnetic anisotropy, a Cu spacer layer, and a Co-free layer with in-plane easy magnetization. By utilizing the spin–orbit torque induced magnetization switching in the synthetic antiferromagnetic layer, the magnetization of the reference layers in the adjacent bridge arms is set to the opposite direction, achieving a GMR sensor with a full Wheatstone bridge structure. The sensor exhibits linear response to the out-of-plane magnetic field with adjustable dynamic ranges from hundreds to thousands of Oe, depending on the thickness of the Co-free layer. A similar Wheatstone bridge sensor consisting of magnetic tunnel junctions was also proposed. The sensor with out-of-plane linear response may have promising applications in three-dimensional magnetic field detection and current sensing field.