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The precise measurement of the W boson mass is closely related to thecontributions of new physics (NP), which can significantly constrain theparameter space of NP models, particularly those with an additional $U(1)$local gauge group. The inclusion of a new $Z'$ gauge boson and gauge couplingsin these models can contribute to the oblique parameters $S$, $T$, $U$ and Wboson mass at tree level. Taking into account the effects of kinetic mixing, wecalculate and analyze the oblique parameters $S$, $T$, $U$ and W boson mass insuch NP models in this study. It is found that the kinetic mixing effects canmake significant contributions to the W boson mass, which can satisfy therecently measured W boson mass at CDF II or ATLAS by choosing appropriatevalues of gauge coupling constants and extra $U(1)$ group charges of leptons orscalar doublets. In addition, if the leptonic Yukawa couplings are invariantunder the extra $U(1)$ local gauge group, these contributions can be eliminatedby redefining the gauge boson fields through eliminating the neutral currentsinvolving charged leptons, even with nonzero kinetic mixing effects.

W boson mass in the NP models with extra $U(1)$ gauge group