A possible mechanism of paramagnetic Meissner effect observed in some high-temperature superconductors is proposed. It is shown that a paramagnetic Meissner current flows if there exists a large quasi-particle density of states around zero energy in the energy gap. This suggests that the paramagnetic Meissner effect is associated with a zero-bias conductance peak which has often been observed in the tunneling experiments of high-temperature superconductors. The paramagnetic effect caused by the zero-energy excitations is consistent with the experiments.