Summary: We study the existence of positive solutions for the singular fractional boundary value problem \[ \begin{gathered} -D^\alpha u(t)= Af(t,u(t))+ \sum^k_{i=1} B_i I^{\beta_i} g_i(t, u(t)),\quad t\in (0,1),\\ D^\delta u(0)= 0,\quad D^\delta u(1)= aD^{{\alpha-\delta-1\over 2}} (D^\delta u(t))|_{t=\xi},\end{gathered} \] where \(1<\alpha\leq 2\), \(0<\xi\leq 1/2\), \(a\in[0,\infty)\), \(1< \alpha- \delta< 2\), \(0< \beta_i< 1\), \(A\), \(B_i\), \(1\leq i\leq k\), are real constants, \(D^\alpha\) is the Riemann-Liouville fractional derivative of order \(\alpha\). By using the Banach’s fixed point theorem and Leray-Schauder’s alternative, the existence of positive solutions is obtained. At last, an example is given for illustration.