The purpose of this paper is to study the existence and multiplicity of solutions to the following Kirchhoff equation with singular nonlinearity and Riemann-Liouville Fractional Derivative: (Pλ) ( a + b ∫ T 0 |0Dαt (u(t))|pdt )p−1 tDαT ( Φp(0Dαt u(t)) ) = λ1(t) uγ(t) + f (t,u(t)), t ∈ (0,T); u(0) = u(T) = 0, where a ≥ 1, b, λ > 0, p > 1 are constants, 1p < α ≤ 1, 0 < γ < 1, 1 ∈ C([0, 1]) and f ∈ C1([0,T] × R,R). Under appropriate assumptions on the function f , we employ variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ