In this paper, we consider singular boundary value problems for the following nonlinear fractional differential equations with delay: { D α x ( t ) + λ f ( t , x ( t − τ ) ) = 0 , t ∈ ( 0 , 1 ) ∖ { τ } , x ( t ) = η ( t ) , t ∈ [ − τ , 0 ] , x ′ ( 1 ) = x ′ ( 0 ) = 0 , $$\left \{ \textstyle\begin{array}{l@{\quad}l} D^{\alpha}x(t)+\lambda f (t,x(t-\tau) )=0, &t\in(0,1)\backslash \{\tau\}, \\ x(t)=\eta(t), &t\in[-\tau,0], \\ x'(1)=x'(0)=0, \end{array}\displaystyle \right . $$ where 2 < α ≤ 3 , D α denotes the Riemann-Liouville fractional derivative, λ is a positive constant, f ( t , x ) $f(t,x)$ may change sign and be singular at t = 0 , t = 1 , and x = 0 . By means of the Guo-Krasnoselskii fixed point theorem, the eigenvalue intervals of the nonlinear fractional functional differential equation boundary value problem are considered, and some positive solutions are obtained, respectively.