The secondary component of GW190814 with a mass of 2.50-2.67 $M_{odot}$ may be the lightest black hole or the heaviest neutron star ever observed in a binary compact object system. To explore the possible equation of state (EOS), which can support such massive neutron star, we apply the relativistic mean-field model with a density-dependent isovector coupling constant to describe the neutron-star matter. The acceptable EOS should satisfy some constraints: the EOS model can provide a satisfactory description of the nuclei; the maximum mass $M_textrm{TOV}$ is above 2.6 $M_{odot}$; the tidal deformability of a canonical 1.4 $M_{odot}$ neutron star $Lambda_{1.4}$ should lie in the constrained range from GW170817. In this paper, we find that the nuclear symmetry energy and its density dependence play a crucial role in determining the EOS of neutron-star matter. The constraints from the mass of 2.6 $M_{odot}$ and the tidal deformability $Lambda_{1.4}=616_{-158}^{+273}$ (based on the assumption that GW190814 is a neutron star-black hole binary) can be satisfied as the slope of symmetry energy $L leq 50$ MeV. Even including the constraint of $Lambda_{1.4}=190_{-120}^{+390}$ from GW170817 which suppresses the EOS stiffness at low density, the possibility that the secondary component of GW190814 is a massive neutron star cannot be excluded in this study.
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