An image encoding apparatus includes a first selector selecting a prediction-order to sub-blocks obtained by further dividing pixel-blocks obtained by dividing a frame of an input-image-signal from predetermined prediction-orders, a second selector selecting, from prediction-modes regulating a manner of referring to an encoded-pixel when a first-prediction-signal of each-sub-block is generated with reference to the encoded-pixel, the number of prediction-modes used in prediction of the first-prediction-signal, a third selector selecting prediction-modes the number of which is the selected number from prediction-modes to use the prediction-modes in prediction of the first-prediction-signal, a generator generating the first-prediction-signal in the selected prediction order by using the selected prediction-modes the number of which is the selected number to generate a second-prediction-signal corresponding to the pixelblock, and an encoder encoding a prediction-residual-error-signal expressing a difference between an image-signal of the pixel-block and the second-prediction-signal to generate encoded data obtained by the prediction-encoding.