In recent years numerous experimental and numerical studies have been carried out on the second order drift forces acting on moored offshore structures in multi-directional waves. In this paper, the general formulae of the second order wave forces under a multiple directional wave environment are deduced, which evaluate the multi-directional coupling difference and sum frequency full QTF matrices (Method 1). However to store all the directional coupling full QTF matrices due to a number of wave directions and further employ this tremendous amount of information in a time domain analysis procedure seems numerically prohibitive. To overcome this difficulty, based on the conventional Newman's approximation approach for long-crested waves, an extended Newman's approximation approach is introduced to estimate both the in-phase and out-of-phase difference frequency QTF matrices for short crested waves (Method 2).  Employing a simple barge model in finite depth water, the directional coupling wave drift force coefficients calculated by Method 1 and Method 2 are compared, indicating that the proposed extended Newman's approximation approach can produce fairly accurate results for the low-frequency second order loading on offshore structures. Application of this approach in the ANSYS® Aqwa™ time domain analysis program shows that this method is efficient, accurate and has a realistic computer memory requirement. The numerical results of a barge model and a standard LNG tanker model demonstrate the impact of the multi-directional coupling second order wave loads on moored offshore structure systems.