Inflation is a promising scenario to resolve problems of big bang cosmology, such as horizon problem. Although there are a lot of models which realize the inflation, it is natural to explain it in the framework of quantum gravity. In this talk, we consider 11 dimensional M-theory, which consists of the 11 dimensional supergravity and quartic terms of the Weyl tensor, as the theory of quantum gravity, and investigate inflationary cosmology by analyzing the effective action of the M-theory. We will show that the classical solution of the 11 dimensional supergravity does not represent the inflationary expansion, but if we include the quantum corrections, the behavior of the solution around the very early time is modified and the inflationary scenario is realized.