1. An image blur correction apparatus, comprising: a blur correction amount calculation unit configured to calculate a blur correction amount based on a shake amount of the apparatus; an estimation calculation unit configured to calculate an estimated value of the blur correction amount using a blur correction amount calculated up until a previous time; a correction unit configured to correct an image blur by cutting out an image using the blur correction amount or the estimated value; and a determination unit configured to determine whether or not to calculate the estimated value in accordance with a frame rate of a moving image.