An image coding apparatus compressing and encoding image data, includes a frequency converging unit to perform frequency conversion on the image data; a bit-plane encoding unit to perform bit-plane encoding on coefficients obtained from the frequency converting unit; and a code discarding unit to discard codes obtained from the bit-plane encoding unit until a present code amount becomes a predetermined code amount. The code discarding unit includes a first discarding unit to perform the discarding operation on a basis of a first code unit; and a second discarding unit to further perform the discarding operation on a basis of a second code unit that is smaller than the first code unit, if necessary, after the discarding operation on the basis of the first code unit is performed by the first discarding unit.