In the image encoding apparatus, the bus traffic monitoring unit monitors the traffic of the memory bus and when the memory bus is congested, the prediction selector is instructed to select the output from the DC prediction unit. Conversely, when the memory bus is not congested, the prediction selector is instructed to select the output from the AC prediction unit. The memory unit stores therein DC coefficients and AC coefficients outputted from the DCT unit so that AC prediction encoding can be performed.