According to one embodiment, an image encoder configured to write coded image data in a memory includes an encoding module, a write address determining module, and a memory controller. The encoding module divides original image data including a plurality of pixels into a plurality of block lines, divides each block line into a plurality of sub-block lines, encodes the original image data in each sub-block line, and generates a plurality of coded sub-block lines. The write address determining module determines a write address of the memory in each coded sub-block line based on a number of the sub-block lines, an original image data size of the original image data, and image coding rate. The memory controller writes the coded sub-block line in the write address corresponding to the coded sub-block line.