We have performed an angle-resolved photoemission spectroscopy (ARPES) study of BaNi$_2$P$_2$ which shows a superconducting transition at $T_c$ $sim$ 2.5 K. We observed hole and electron Fermi surfaces (FSs) around the Brillouin zone center and corner, respectively, and the shapes of the hole FSs dramatically changed with photon energy, indicating strong three-dimensionality. The observed FSs are consistent with band-structure calculation and de Haas-van Alphen measurements. The mass enhancement factors estimated in the normal state were $m^*$/$m_b$ $leq$ 2, indicating weak electron correlation compared to typical iron-pnictide superconductors. An electron-like Fermi surface around the Z point was observed in contrast with BaNi$_2$As$_2$ and may be related to the higher $T_c$ of BaNi$_2$P$_2$.
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