In this paper, for the fourth-order boundary value problem (BVP) u ( 4 ) ( t ) + η u ″ ( t ) + η 2 4 u ( t ) = f ( t , u ( t ) ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , where f : [ 0 , 1 ] × R → R is continuous, η ≤ 0 is a parameter, the existence of infinitely many mountain pass solutions are obtained with the variational methods and critical point theory. We prove the conclusion by combining sub–sup solution method, Mountain pass theorem in order intervals, Leray–Schauder degree theory and Morse theory.