In this paper, we consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem. D 0 + α u ( t ) + f ( t , u ( t ) ) + e ( t ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , D 0 + β u ( 1 ) = a D 0 + β u ( ξ ) where 1 < α ⩽ 2 , 0 < β ⩽ 1 , 0 ⩽ a ⩽ 1 , 0 < ξ < 1 , α - β - 1 ⩾ 0 , D 0 + α is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular at u = 0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.