Abstract: In the present work, we study the effect of the isovector scalar meson a_0(980) (also called \delta) to the asymmetric matter properties by constructing a parity doublet model with including the a_0(980) meson based on the approximate chiral U(2)_L × U(2)_R symmetry. The effect of a_0(980) to the properties of symmetric matter such as symmetry energy S(n_B), symmetry incompressibility K_\rmsym, symmetry skewness Q_\rmsym is investigated. We find that, a_0(980) meson has significant effect to these nuclear matter properties especially when the chiral invariant mass of nucleon m_0 is small. We also study the effect of the a_0(980) meson to the neutron star (NS) properties and find that it increase the radius of NSs, especially those having intermediate mass. Finally, we further constrain the value of the chiral invariant mass of the nucleon to 640 \,\text MeV \lesssim m_0 \lesssim 860 \,\text MeV for L_0 = 57.7 MeV by comparing with the recent accepted value of K_\rmsym and neutron star (NS) observational data.