The magnetoelectric (ME) effect, the induction of electric polarization (P) by an applied magnetic field or magnetization (M) by an electric field, provides a new pathway for the low-power-consumption data memory devices. In this work, we present a systematic experimental investigation of the magnetism, heat capacity, and anisotropic ME effect in BaNi2(PO4)2 single crystals. Our results reveal a long-range antiferromagnetic ordering below the Néel temperature TN = 24 K, where the Ni2+ spins are antiferromagnetically aligned along the x // [1-10] axis. Detailed ME measurements reveal that BaNi2(PO4)2 exhibits dominant out-of-plane electric polarization and significant in-plane electric polarization along the y // [110] direction. The largest magnetically induced electric polarization of 128 C/m2 along the z // [001] axis is observed at T = 2 K under the magnetic field of 0H = 9 T applied along the x direction, with a ME coefficient of   16.8 ps/m. The angular dependent measurement demonstrates that the induced in-plane electric polarization Py changes its direction by an -2 around the z axis upon rotating the magnetic field H by an angle . Based on the crystal and magnetic symmetry of the honeycomb layer, the microscopic origin of in-plane electric polarization Px and Py under H // z and Py under H // x and H // y can be attributed to the inverse Dzyaloshinskii-Moriya mechanism and the spin dependent p-d hybridization mechanism, respectively. Thus, this work provides insights to understand the microscopic origin of the ME coupling in linear magnetoelectric materials.