Disclosed herein is a spring structure having a contact-preventing and rigidity-reinforcing function for a bed mattress in which the structure of a connection end portion for connecting a body spring and an exposure wire spring to each other is improved such that the connection end portion is not in close contact with an uppermost winding and/or a lowermost winding of the body spring and such that when a load is exerted to an exposure wire spring a displacement is prevented from being generated in which the exposure wire spring is leaned to one side, and rigidity of the spring is reinforced so that the exposure wire spring ascends/descends vertically only, thereby easily preventing the lateral displacement and deformation of the spring along with a prevention of a noise due to a frictional contact to prolong the lifespan of the spring.