Summary: In this paper, we study the existence of positive solutions to boundary value problem for fractional differential system \[ \begin{cases} D^\alpha_{0^+}u(t) + f_1(t,u(t),v(t)) = 0,\quad t\in(0,1),\\ D^\alpha_{0^+}v(t) + f_2(t,u(t),v(t)) = 0,\quad t\in(0,1),\,t <\alpha\leqslant 2, \\u(0) = 0, \quad D^\beta_{0^+} u(1) -\mu_1D^\beta_{0^+}u(\eta_1) =\lambda_1,\\v(0) = 0, \quad D^\beta_{0^+}v(1)-\mu_2D^\beta_{0^+}v(\eta_2) =\lambda_2, \quad 0 <\beta < 1,\end{cases} \] where \(D^\alpha_{0^+}\) is the Riemann-Liouville fractional derivative of order \(\alpha\). By using the Leggett-Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained.