  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.
