Relational data can generally be represented as graphs. For processing such graph structured data, we propose LanczosNet, which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of matrix power but also design learnable spectral filters. We benchmark our model against 8 recent deep graph networks on QM8 quantum chemistry dataset. Experimental results show that our model achieves the state-of-the-art performance.