Image encoding apparatus

An Image Encoding Apparatus converts image data using discrete cosine transformation. A block forming means (26) forms blocks of data and a plurality of code quantity estimating means (40A-40D) estimate amounts of code by coding the data of the blocks, each using respective different quantization steps. A quantization matrix generation means (36) provides a common quantization matrix (W) to each of the code quantity estimation means. The data is encoded by variable length coding using a quantization step derived from the code quantity estimation means operating on data from a previous frame.