Black phosphorus (BP) is a semiconducting material with a direct finite band gap in its monolayer, attracting intense attention for its application in field-effect transistors. However, strong Fermi level pinning (FLP) has been observed for contacts between BP and high work function metals, e.g., Cu. Such FLP presents an undesirable hurdle preventing the achievement of high performance field-effect devices. In this regard, there is a crucial need to understand the FLP occurring at the metal-BP interfaces and explore the possibility to reduce it. The present work studied atomic passivation in reducing FLP for the Cu-BP system using density functional theory calculations. The passivation by H, N, F, S, and Cl atoms on the Cu(111) surface has been considered. The results showed that the passivated atoms can shield the direct contact between Cu(111) and BP, thus reducing FLP at Cu-BP interfaces. In particular, S and Cl atoms were found to be highly effective agents to achieve a significant reduction of FLP, leading to Cu-BP contacts with ultralow Schottky barrier height (SBH) and suggesting the possibility of ohmic contact formation. Our findings demonstrate surface passivation as an effective method towards depinning the Fermi level at the metal-BP interface and subsequently controlling the SBH for BP-based electronic devices.