Factorization Machines (FMs), a general predictor that can efficiently model high-order feature interactions, have been widely used for regression, classification and ranking problems. However, despite many successful applications of FMs, there are two main limitations of FMs: (1) FMs consider feature interactions among input features by using only polynomial expansion which fail to capture complex nonlinear patterns in data. (2) Existing FMs do not provide interpretable prediction to users. In this paper, we present a novel method named Subspace Encoding Factorization Machines (SEFM) to overcome these two limitations by using non-parametric subspace feature mapping. Due to the high sparsity of new feature representation, our proposed method achieves the same time complexity as the standard FMs but can capture more complex nonlinear patterns. Moreover, since the prediction score of our proposed model for a sample is a sum of contribution scores of the bins and grid cells that this sample lies in low-dimensional subspaces, it works similar like a scoring system which only involves data binning and score addition. Therefore, our proposed method naturally provides interpretable prediction. Our experimental results demonstrate that our proposed method efficiently provides accurate and interpretable prediction.