An image coding apparatus for coding image data. The image coding apparatus includes: a first coding mechanism predicting a quantization parameter and a quantization matrix to be used for calculating a target amount of code for the image data by coding the image data; a second coding mechanism correcting the quantization parameter predicted by the first coding means from an error between an amount of generated code produced by coding using the quantization parameter and the quantization matrix predicted by the first coding mechanism and the target amount of code; and a third coding mechanism coding the image data using the quantization parameter corrected by the second coding mechanism.