An image coding apparatus executes intra-frame prediction with a predetermined intra-frame prediction mode for a certain block. A block selection unit judges that the current block to be coded is a prediction error calculation block or a non-prediction error calculation block. In the case where the current block is a prediction error calculation block, a mode error value calculation unit calculates the prediction error by the sum of absolute differences and for all of the intra-frame prediction modes, an inter-mode comparison unit compares the prediction errors, and as a result of the comparison, an intra-frame prediction mode having the minimum prediction errors is determined as the intra-frame prediction mode. In the case where the current block is a non-prediction error calculation block, the prediction error is not calculated. As an alternative, a prediction mode estimation unit determines the intra-frame prediction mode based on the neighboring prediction mode information stored in a storage unit.