In this paper, we consider a nonautonomous Choquard equation with singularity{−Δu+V(x)u=λ(Iα⁎|u|p)|u|p−2u+f(x)u−γ,x∈R3,u>0,x∈R3, where Iα is the Riesz potential of order α∈(0,3) and λ>0, 1+α3≤p<3+α, 0<γ<1. Under certain assumptions on V and f, the existence and multiplicity of positive solutions are obtained by using variational method and structure of associated Nehari manifold. We also study the asymptotical behavior of solutions as λ→0.