Abstract Existing deep neural networks mainly focus on learning transformation invariant features. However, it is the equivariant features that are more adequate for general purpose tasks. Unfortunately, few work has been devoted to learning equivariant features. To fill this gap, in this paper, we propose an affine equivariant autoencoder to learn features that are equivariant to the affine transformation in an unsupervised manner. The objective consists of the self-reconstruction of the original example and affine transformed example, and the approximation of the affine transformation function, where the reconstruction makes the encoder a valid feature extractor and the approximation encourages the equivariance. Extensive experiments are conducted to validate the equivariance and discriminative ability of the features learned by our affine equivariant autoencoder