The invention provides a rail friendly type anti-yaw oil pressure damper. The rail friendly type anti-yaw oil pressure damper comprises a piston rod end part connecting part, a dustproof cover, a rubber dustproof sleeve, a dustproof ring, an inner cap nut, a framework oil seal, an outer cap nut, a guide bearing end part sealing part, a guide bearing assembly, a guide bearing gas exhaust plate, a pressure cylinder barrel, a piston-piston rod assembly, an oil storage cylinder assembly, hydraulic oil, a bottom valve assembly, a pressure cylinder barrel gasket, a bottom valve gasket, an oil guide plate assembly, a small magnet and an oil return assembly. The two sides of a middle area of the inner wall of the pressure cylinder barrel of the oil pressure damper are equipped with symmetrical bypass damping slots; and when a position, passing through a curve, a bogie and a vehicle body, of a train changes, the oil pressure damper has a damping self-adapting function, and can effectively reduce wheel rail acting force and abrasion. The rail friendly type anti-yaw oil pressure damper avoids the defects that an active control type anti-yaw oil pressure damper system is complex, is poor in reliability and real-time property, is high in manufacturing cost and is difficult to maintain, and also achieves the effects of having a damping coefficient varying function and being safe and reliable. The invention further provides a low damping parameter design method for the rail friendly type anti-yaw oil pressure damper.