In this paper, we consider singular boundary value problems for the following nonlinear fractional differential equations with delay: $$\left \{ \textstyle\begin{array}{l@{\quad}l} D^{\alpha}x(t)+\lambda f (t,x(t-\tau) )=0, &t\in(0,1)\backslash \{\tau\}, x(t)=\eta(t), &t\in[-\tau,0], x'(1)=x'(0)=0, \end{array}\displaystyle \right . $$ where $2<\alpha\leq3$ , $D^{\alpha}$ denotes the Riemann-Liouville fractional derivative, λ is a positive constant, $f(t,x)$ 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.