An image data compressing apparatus includes an image data compressor for compressing image data input thereto at first and second compression rates to produce first and second compressed data, respectively, an approximate-expression selector having an approximate-expression table including approximate expressions corresponding to sample data sizes, respectively, and a compression rate determining unit for determining the second compression rate. The approximate-expression selector selects an approximate expression from the approximate expressions. The first approximate expression corresponds to a first sample data size nearest a data size of the first compressed data among the sample data sizes. Each of the approximate expressions indicates a change of a data size in response to a compression rate. The compression rate determining unit determines the second compression rate based on the selected approximate expression. The image data compressing apparatus provides a desired size of the compressed image data by maximum two of the compressing operations.