For the entropy coding of image data after subjected to orthogonal transforation and quantization, a plurality of entropy coding units are provided in parallel. The plurality of entropy coding units can be operated efficiently and the entropy coding can be executed at high speed. In order to realize these operations, for example, an entropy coding apparatus has: an orthogonal transformation unit for performing an orthogonal transformation of image data; a quantization unit for quantizing coefficients obtained by the orthogonal transformation; N entropy coding units for entropy-coding the quantized coefficients output from the quantization unit; a distribution unit for selecting one of the N entropy coding units for each quantized coefficient and supplying the quantized coefficient to the selected entropy coding unit; and a prediction unit for monitoring a coding state of each of the N entropy coding units and predicting an optimum one of the N entropy coding units for a succeeding quantized coefficient in accordance with monitor results.