1. A moving image encoding apparatus for performing encoding using inter prediction between frames, comprising: a predicted image generating unit configured to generate a predicted image for the inter prediction; a transforming unit configured to divide an original image into blocks each having a predetermined number of pixels, and for performing orthogonal transformation and quantization on a difference between an encoding target image and the predicted image for each of the blocks; an encoding unit configured to generate an encoded stream by encoding a transformation result from said transforming unit; a locally decoding unit configured to generate a locally decoded image by performing inverse quantization and inverse orthogonal transformation on the transformation result from said transforming unit; a filter processing unit configured to perform deblocking filter processing on the locally decoded image, and providing the locally decoded image having undergone the deblocking filter processing to said predicted image generating unit; an image quality deterioration degree calculating unit configured to calculate an image quality deterioration degree from the original image and the locally decoded image; and a filter intensity determining unit configured to determine a filter intensity to be used in the deblocking filter processing, based on the calculated image quality deterioration degree, and a difference value between adjacent boundary pixels of the locally decoded image and another locally decoded image adjacent to the locally decoded image.