A copolymer and preparation method and application thereof are disclosed. The copolymer is random copolymer obtained from monomers consisting of acrylamide, acrylic acid, alkenyl sulfonate, 2-acrylamido-dodecyl sulfonate, p-styrene sulfonate or isoprene sulfonate and so on. The copolymer of present invention can be used as fluid loss additive and has good fluid loss properties, which would not make the drilling fluid thicken at high temperature of 200° C. and high salt conditions of saturated brine. It has a medium-pressure fluid loss after aging and rolling for 16 h at high temperature of 200° C., as measured in accordance with the American Petroleum Institute Standard Test at room temperature, and has good properties of high temperature-resisting and salt-resisting.