A relief valve for an oil pump can prevent a main gallery from being damaged by largely decreasing peak pressure of an oil pump by using bypass flow according to oil pressure of the main gallery in cold start of an engine, and can control the discharging pressure of the oil pump at the optimum level when the engine is warmed up, by defining a housing chamber communicating with the main gallery of the engine and a plunger chamber bypassing some of oil flowing to the main gallery to the oil pump or an oil pan in accordance with oil pressure in the housing chamber using a plunger chamber, and by changing a modulus of elasticity of a coil spring elastically supporting the plunger in accordance with the oil pressure produced in the main gallery, by using a substance that is expanded by temperature.