This paper develops a two-dimensional implicit particle-in-cell model, which considers algorithms without and with magnetic field, based on the anisotropic immersed-finite-element method. The direct implicit particle-in-cell (DIPIC) algorithm is utilized to track the movement of electrons and ions, while the anisotropic immersed-finite-element method is developed to compute the electric field. Compared with the previous works, the immersed-finite-element direct implicit particle-in-cell (IFE-DIPIC) method developed in this article can use larger temporal and spatial step sizes to simulate the plasma problems and can handle the complex interface problems on a Cartesian mesh independent of the interface. Hence, the IFE-DIPIC method can significantly improve the computational efficiency, especially for the large-scale and long-time evolution plasma problems with complex interface. Numerical experiments are provided to demonstrate the proposed method and show the applicability in the simulations of plasma sheath problems.