  The holographic dark energy model is one of the important ways for dealing
with the dark energy problems in the quantum gravity framework. In this model,
the dimensionless parameter $c$ plays an essential role in determining the
evolution of the holographic dark energy. In particular, the holographic dark
energy with $c\geq 1$ can be effectively described by a quintessence
scalar-field. However, according to the requirement of the weak gravity
conjecture the variation of the quintessence scalar-field should be less than
the Planck mass, which would give theoretic constraints on the parameters $c$
and $\Omega_{\mathrm{m0}}$. Therefore, we get the possible theoretical limits
on the parameter $c$ for the holographic quintessence model.
