Abstract: The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius. In particular, the compact object with a mass of 2.50 \sim 2.67 \; M_\odot observed by LIGO Scientific and Virgo collaborations in GW190814, as well as the recent report of a light compact object with a mass and radius of M=0.77^+0.20_-0.17M_\odot and R=10.4^+0.86_-0.78 km within the supernova remnant HESS J1731-347, have posed a great challenge to the investigations into the supranuclear matter. In the inner core of a neutron star, the strangeness degrees of freedom, such as the hyperons, can be present to form a hyperon star. In this work, the neutron star consisting of nucleons and leptons, and the hyperonic star including the hyperons will be studied in the framework of the density-dependent relativistic mean-field (DDRMF) model. Some popular DDRMF parameterizations will be adopted to investigate the properties of nuclear matter and the mass, radius, tidal deformability, and other properties of neutron star and hyperonic stars. We find that the maximum masses of neutron star calculated by DD-MEX, DD-MEX1, DD-MEX2, DD-MEXY and DD-LZ1 sets can be around 2.5 \sim 2.6 \; M_\odot because they can produce quite stiff equations of state (EOSs) due to the strong repulsive contributions from vector potentials at high densities. Moreover, by investigating the influence of the crust EOS and core EOS on the neutron stars, we find that the observational data from HESS J1731-347 suggest the requirement of a crust EOS with a higher L parameter and a core EOS with a lower L parameter, and the M-R relations from the constructed EOSs can also be consistent with the observables of PSR J0740+6620, PSR J0030+0451 from NICER and the GW170817 event. With the inclusion of hyperons, the hyperonic star matter becomes softer compared to the neutron star matter, but the massive hyperonic star can also be obtained with DDRMF parameter sets if the vector meson coupling constants are strong.