An image compressing apparatus carrying out code amount control upon JPEG2000 coding, in which the number of coding passes and a code amount for each code block generated by a MQ (arithmetic) coder are input, and the number of coding passes and the code amount are determined based on a first code amount control standard and a second code amount control standard given for each code block. For a specific code block, the second code amount control standard is used to determine the number of coding passes and the code amount, while, for the other code blocks, the first code amount control standard is used to determine the number of coding passes and the code amount.