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The Regular Phantom Black Hole (RPBH)s are of theoretical and observational importance, some of their properties have been studied. In this work, some of thermodynamical properties such as entropy, temperature, etc., in three background cases, that is, flat, de–Sitter (dS) and Anti–de Sitter (AdS) are studied. Many of the RPBH properties, including horizon radius, are (directly or indirectly) dependent on a scale parameter b$b$. Due to the slightly different structure from Schwarzschild—like metrics, the method to express relations between thermodynamical variables requires a new function of the scale parameter. The local and global stability through the Heat Capacity (HC) and Gibbs free Energy (GE), respectively are also treated. In the AdS case, the regularized metric allows a Hawking‐Page like phase transition of first order. The calculations and graphs show the results in the flat background, are very similar to Schwarzschild black hole and the asymptotically AdS RPBH is more compatible with physical laws than the dS and flat backgrounds. [ABSTRACT FROM AUTHOR]