Summary: In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by \(HS_p(\lambda)\), and its subclass \(HS_p^0(\lambda)\), where \(\lambda \in [0,1]\) is a constant. These classes are natural generalizations of a class of mappings studied by A. W. Goodman [Proc. Am. Math. Soc. 8, 598–601 (1957; Zbl 0166.33002)] in 1950’s. We generalize the main results of Y. Avci and E. J. Złotkiewicz [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 44, 1–7 (1990; Zbl 0780.30013)] from 1990’s to the classes \(HS_p(\lambda)\) and \(HS_p^0(\lambda)\), showing that the mappings in \(HS_p^0(\lambda)\) are univalent and sense preserving. We also prove that the mappings in \(HS_p^0(\lambda)\) are starlike with respect to the origin, and characterize the extremal points of the above classes.