The configuration interaction (CI) is a versatile wave function theory for interacting fermions, but it involves an extremely long CI series. Using a symmetric tensor decomposition method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested by using small molecules. Provided that the length of the symmetric tensor decomposition CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full CI with enhanced practicability.