We study the masses of $\bar{D}$ $(0^+)$ meson and $\bar{D}$ $(0^+)$ meson, and spectral function for $\bar{D}_0^*$ meson channel in nuclear matter. These mesons are introduced as chiral partner to each other as probes to explore the partial restoration of chiral symmetry in nuclear matter. Our calculations show that the mass difference between $\bar{D}$ meson and $\bar{D}_0^*$ meson gets small as the baryon number density increases, which reflects the partial restoration of chiral symmetry. In the spectral function for $\bar{D}_0^*$ meson channel, we find three peaks. First peak corresponds to the resonance of $\bar{D}_0^*$ meson and this peak is broadened by collisions with nucleons, and peak position shifts to lower energy due to the partial restoration of chiral symmetry. Second peak corresponds to the threshold enhancement, and this peak shifts to higher energy and its height is remarkably enhanced. Third peak is identified as the Landau damping, and this peak grows gradually as the density increases. These modifications are the consequences of partial restoration chiral symmetry in nuclear matter.