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Stimulated by the recent researches of black hole thermodynamics for blackhole with Newman-Unti-Tamburino (NUT) parameter, we investigate thethermodynamics and weak cosmic censorship conjecture for a Kerr-Newman Taub-NUTblack hole. By defining the electric charge as a Komar integral over the eventhorizon, we construct a consistent first law of black hole thermodynamics for aKerr-Newman Taub-NUT black hole through Euclidean action. Having the first lawof black hole thermodynamics, we investigate the weak cosmic censorshipconjecture for the black hole with a charged test particle and a complex scalarfield. We find that an extremal black hole cannot be destroyed by a chargedtest particle and a complex scalar field. For a near-extremal black hole withsmall NUT parameter, it can be destroyed by a charged test particle but cannotbe destroyed by a complex scalar field.

First law of black hole thermodynamics and the weak cosmic censorship conjecture for Kerr-Newman Taub-NUT black holes