Subspace clustering is a challenging problem in large-scale datasets due to the high computational cost associated with the coding and spectral decomposition. To address the above challenge, we introduce a novel approach, fully parametric subspace clustering (FPSC), that transforms the subspace clustering into learning neural network based classifier. Specifically, FPSC consists of three sequential networks: 1) a neural base-expressive model for learning low-dimensional coefficients, 2) a neural network for approximating the eigenvectors of the affinity matrix of the coefficients, and 3) a neural classifier that is trained with pseudo-labels generated by clustering the eigenvectors. Furthermore, we provide the theoretical analysis to demonstrates an upper bound on the reconstruction error. Experimental results demonstrate that our method significantly outperforms state-of-the-art subspace clustering methods.