According to one embodiment, an encoding apparatus includes a prediction unit, a classifying unit, a first transformer, a second transformer, an order controller, and an entropy coder. The prediction unit obtains a predictive residual signal to be encoded, by using a mode selected from intra-prediction modes. The first transformer obtains first transformation coefficients by subjecting the signal to an orthogonal transformation by use of a first transformation basis if the selected mode is classified into a mode having a prediction direction. The first transformation basis is preset so that a coefficient density after the orthogonal transformation is higher than a coefficient density.