It is aimed at decreasing process load for arithmetic coding and effectively providing rate control by suppressing image quality degradation. In an image encoding apparatus 1, a code amount adding section 18 accumulates code amounts of arithmetic codes D17 for each bit plane encoded in an EBCOT section 17 and supplies an accumulated value to a control section 19. The control section 19 compares this accumulated value with a targeted code amount. When the accumulated value does not reach the targeted code amount, the control section 19 transmits a control signal D19 to the EBCOT section 17 to encode the next bit plane. When the accumulated value reaches the targeted code amount, the code amount adding section 18 supplies an encoded code stream D20 after completion of the code amount control to a header generation section 20 and a packet generation section 21. At this time, the EBCOT section 17 encodes a quantization coefficient D15 for each bit plane by traversing all code blocks from a bit plane having the highest bit position to a bit plane having the lowest bit position in order.