Motivated by recent observational data, the equations of state with the inclusion of strangenessbearing Λ-hyperons and the corresponding properties of neutron stars are studied, based on the covariant density functional (CDF) theory. To this end, we specifically employ the density dependent relativistic Hartree-Fock (DDRHF) theory and the relativistic mean field theory (RMF). The inclusion of Λ-hyperons in neutron stars shows substantial effects in softening the equation of state. Because of the extra suppression effect originated from the Fock channel, large reductions on both the star mass and radius are predicted by the DDRHF calculations. It is also found that the mass-radius relations of neutron stars with Λ-hyperons determined by DDRHF with the PKA1 parameter set are in fairly good agreement with the observational data where a relatively small neutron stars radius is required. Therefore, it is expected that the exotic degrees of freedom such as the strangeness-bearing structure may appear and play significant roles inside the neutron stars, which is supported further by the systematical investigations on the consistency between the maximum neutron star mass and Λ-coupling strength. As the natural laboratories in the universe for nuclear and particle physics, neutron stars [1] have fascinated much effort concentrated on exploring the equation of state (EoS) of baryonic matter at low temperature and high density [2,3]. Specifically the mass of the observed neutron stars brings a strong constraint on the behavior of EoS at supranuclear density. The most precise measurements for the neutron star mass are determined to be less than 1.5M from the timing observations of radio binary pulsars [4], which has remained for many years to constraint the EoS. However, the existence of more massive compact stars is now unveiled by some evidence [5]. In a survey with the Arecibo telescope, an eccentric binary millisecond pulsar PSR J1903+0327 was found with an unusually high mass value (1.74 ± 0.04)M [6]. Recently a much larger pulsar mass of (1.97 ± 0.04)M was measured using Shapiro delay for the binary millisecond pulsar J1614-2230 [7]. All of these new data imply a stiff EoS of strongly interacting matter at high densities, which need further check on the new developed land-and space-based observatories.So far, there still exists considerable theoretical uncertainty on the EoS at supranuclear densities due to the poorly constrained many-body interaction, consequently deducing very different maximum mass and radius for a beta-stable neutron star. As indicated by prior study of neutron star based on the density dependent relativistic Hartree-Fock (DDRHF) theory [8], the maximum mass predicted by the covariant density functional (CDF) cal- * Electronic address: longwh@lzu.edu.cn culations [9,10] lies between 2M and 2.8M . The Corresponding EoSs deviate remarkably from each other at high density region. In the center of neutron stars, the density is generally considered as high as 5 to 10 times the nuclear equilibrium (satu...