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[en] Highlights: • The Palladium monotelluride (PdTe) with hexagonal structure (P63/mmc) has renewed a big interest recently. But there is a contradiction in the recent investigations on the electron-phonon interaction in hexagonal PdTe. The theoretical study can give precise interaction on superconductivity. • In order to ensure calculated results to be more reliable, the first‐principles calculations with both the Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) are used. • On the calculated data we found that the hexagonal PdTe superconductor is in the intermediate coupling regime, rather than previous thoughts that it is a strongly coupled (Karki A B, et al. 2012 J. Phys.: Condens. Matter 24 055701) or a weakly coupled superconductor (Tiwari B, et al. 2015 Supercond. Sci. Technol. 28 055008). - Abstract: The electronic structure, phonons and electron-phonon interaction of hexagonal PdTe have been investigated in detail by employing a plane wave pseudopotential method and a linear-response scheme within Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA). Consistent with available theoretical and experimental results, it has been found that the intermediate strength electron-phonon coupling constant (λ) with the calculated value of 0.542 on the LDA and 0.648 on the GGA is due to the coupling of phonons from Pd and Te atoms and electrons from Pd-d and Te-p states. Through comparison, the calculations on the GGA produce better quality than that on the LDA. On the basis of appropriate Coulomb pseudopotential (μ"∗) and λ of 0.648 together with experimental Debye temperature (Θ), via the McMillan formula, the superconducting transition temperature with the value of 4.5 K is obtained, same to the experimental value. The results indicate that conventional electron–phonon coupling mechanism can explain the superconductivity in this compound.