Image processing apparatus for generating an image having an expanded dynamic range and method thereof, and image capture apparatus

An image capture apparatus generating an image, a dynamic range of which is expanded by composing two images having different exposure amounts, includes an imaging unit which continuously outputs images captured to have two different exposure amounts. A system control unit of the image capture apparatus stores in a memory an image of the first frame of two frames to be composed, which are continuously output from the imaging unit, and composes an image of the second frame output from the imaging unit and the image held in the memory so as to expand a dynamic range. The system control unit generates tone compression characteristics based on the image held in the memory and an image obtained by reducing a resolution of the held image, and compresses tones of the composed image using the generated tone compression characteristics.