In this paper, we study the vector penalty-projection method for incompressible unsteady Stokes equations with Dirichlet boundary conditions. The time derivative is approximated by the backward difference formula of second-order scheme (BDF2), namely Gear's scheme, whereas the approximation in space is performed by the finite volume scheme on a Marker And Cell (MAC) grid. After proving the stability of the method, we show that it yields second-error estimates in the time step for both velocity and pressure in the norm of l ∞ (L 2 (Ω)) and l 2 (L 2 (Ω)) respectively. Besides, we show that the splitting error for both velocity and pressure is of order O(√ ε δt) where ε is a penalty parameter chosen as small as desired and δt is the time step. Numerical results in agreement with the theoretical study are also provided.