1. An image processing apparatus which reduces an image-shake of an image caused by a shake of an image pickup apparatus, the image processing apparatus comprising: a shake detector configured to detect the shake applied to the image pickup apparatus; a shake analyzer configured to obtain features of a plurality of shake components whose kinds are different from each other, the features included in the shake detected by the shake detector; a parameter calculator configured to calculate a filtering process parameter depending on the features for each of the shake components; and a processor configured to perform a filtering process using the filtering process parameter calculated for each of the shake components to calculate a shake reduction amount and perform a shake reduction process based on the shake reduction amount with respect to the image.