In this study, we present a compression algorithm to solve quantum field eigenvalue problems with dramatically reduced memory requirements. We represent light-cone quantized basis states as 2D matrices, in which one index stands for longitudinal momenta and the other represents transverse momenta. These matrices are stored as singular value decompositions, compressed to retain only the n<sub>svd</sub> largest contributions. Basic Lanczos iterations are applied to obtain eigenvalues. At each Lanczos iteration, each sector of the Lanczos vector is projected into n<sub>svd</sub> longitudinal and transverse vectors using singular value decomposition. The converged smallest real eigenvalues are obtained by these Lanczos iterations. The convergence of the ground state with respect to n<sub>svd</sub> is then studied. It shows that our compression algorithm reduces memory cost significantly with little sacrifice in the accuracy of calculations.