  We describe a simple method to find the ground state energy without
calculating the expectation value of the Hamiltonian in the time-evolving block
decimation algorithm with tensor network states. For example, we consider
quantum many-fermion systems with matrix product states, which are updated
consistently in a way that accounts for fermion exchange effects. This method
can be applied to a wide class of fermion systems. We test this method in
spinless fermion system where the exact ground state energy is known. We
analyze finite size effects to determine the ground state energy in the
thermodynamic limit that is compared to the exact value.
