Abstract: By applying Leggett-Williams fixed point theorem,the fourth-order three-point boundary value problem is studied: u^(4)(t)=f(t,u(t))\quad ~(t\in 0,1), u'(0)=u''(\eta)=u'''(0)=u(1)=0, where~f:0,1\times0,+\infty )\rightarrow0,+\infty)~is continuous,~\eta\in\frac\sqrt33,1.~The existence of at least~2m-1~positive solutions for arbitrary positive integer m is obtained while the problem has the sign-changing Green's function.