We investigate the effects of the light vector U-boson that couples weakly to nucleons in relativistic mean-field models on the equation of state and subsequently the consequence in neutron stars.It is analyzed that the U-boson can lead to a much clearer rise of the neutron star maximum mass in models with the much softer equation of state.The inclusion of the U-boson may thus allow the existence of the non-nucleonic degrees of freedom in the interior of large mass neutron stars initiated with the favorably soft EOS of normal nuclear matter.In addition, the sensitive role of the U-boson in the neutron star radius and its relation to the test of the non-Newtonian gravity that is herein addressed by the light U-boson are discussed[1].