In an image encoder, a first quantization section which is selected when normal image quality is required performs quantization by dividing a wavelet transformation coefficient by a quantization step size and by thereafter rounding down a fraction thereof. On the other side, a second quantization section which is selected when high image quality is required performs quantization by dividing a wavelet transformation coeffient by a quantization step size, by adding 0.5 to the dividing result, and by thereafter rounding down a fraction thereof. Therefore, the width of a dead zone where coefficients are quantized to a value of 0 is narrower than that in the first quantization section, and higher image quality is obtained accordingly.