In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions:D0+αu(t)+h(t)f(t,u(t))=0,0<t<1,u(0)=u′(0)=u″(0)=0,u(1)=λ∫0ηu(s)ds,where 3<α≤4,0<η≤1,0⩽ληαα<1,D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution.