To prove Yau's Uniformization Conjecture, Wan-Xiong Shi initiated studying the Ricci flow on complete noncompact Riemannian manifolds. The first important thing in the study of the Ricci flow on Riemannian manifolds which we have to consider is the short-time existence of the solution. In this talk, using Deane Yang's local Ricci flow, we prove the short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. As a corollary of our main theorem, we get the short-time existence part of Shi's theorem in this more general context.