Abstract: The study of exotic nuclei is one of the most interesting frontier topics in nuclear physics. There are relatively few studies on the existence of halo in medium-mass nuclei. The complex momentum representation(CMR) method can be used to explore exotic structures in nuclei. The resonant states near the continuum threshold play an important role in the formation of exotic phenomena. Therefore, the relativistic point coupled and the complex momentum representation (RMFPC-CMR) method is used to explore the exotic structures for the neutron-rich Cr isotopes. The two-neutron separation energies have been calculated to be very close to zero, and the mean square (rms) radii of neutron also have increased sharply, implying the presence of halo structures in the Cr isotopes near the neutron drip line. The single-particle levels, the occupation probabilities of valence nucleons on the levels near the Fermi surface, the neutron and proton density distributions, and the contribution of every level to the nucleus density are obtained, it can be found that the occupations of the levels 3s_1/2 and 2d_3/2 are beneficial to the formation of neutron halo. It is found that the unusual increases of rms radii and diffuse distributions of neutron densities come mainly from the contributions of the weakly bound levels with lower orbital angular momentum, which leads to the neutron halos of ^76-82Cr near the neutron drip line. This prediction has a certain reference value for exploring the halo nuclei in the medium mass region in experiments.