Abstract: A manifold is a topological space such that each point is in an open set which is diffeomorphic to an Euclidean ball. A basic problem in Riemannian geometry is to, for a metric on a manifold, estimate the largest radius (in terms of curvature conditions) such that any metric ball of this radius is diffeomorphic to an Euclidean ball. This radius is called the injectivity radius of the metric. This talk concern with the estimate of the injectivity radius of a metric whose sectional curvature is bounded between two positive numbers.