We study the thermodynamics of the Taub-NUT AdS black holes by Visser
    holographic method using AdS radius as a constant parameter under the
    restricted phase space approach. Instead of the variables $P$ and $V$, we deal
    with the central charge and also chemical potential as a unique couple of
    conjugate thermodynamic variables. We study some interesting properties of the
    Taub-NUT black holes e.g. supercritical phase equilibrium in the $T-S$
    processes, $Q-\Phi$ and the Hawking-Page phase transition in the $\mu-C$
    processes. As a consequence, the consistency of the weak gravity conjecture of
    multi-charge for Taub-NUT-AdS black holes at critical points is proved. We
    conclude that in the presence of the central charge and assuming
    $C=\frac{3}{8}\ell^2$, weak gravity conjecture could be satisfied in the
    Taub-NUT-AdS black holes with $\hat{n}\ll 1$.

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