Directional couplers are basic components for forming various kinds of photonic devices. In this paper, a directional coupler composed of two horizontal multiple-slotted waveguide structures with slanted sidewalls is characterized by using a full-vectorial finite element method in terms of the electric fields. The effective indexes of the even and the odd modes and the corresponding coupling lengths, both in quasi-TE and quasi-TM modes, are presented, where the strongly-hybrid nature of the guided-mode is effectively demonstrated. The results show that the coupling lengths in quasi-TE and quasi-TM modes exponentially increase with the increase of the gap between the coupled waveguides, where the value in quasi-TE mode is more sensitive to the variation of the angle of the sidewall, while the value in quasi-TM mode is more sensitive to variation of the height and the index of the slot. Properly choosing the structure and material parameters, polarization-independent directional couplers can be realized.