The 2-D/1-D concept is widely used in various neutron transport codes to obtain sub-pin level flux distribution. The 3D problem is decomposed into 2-D plane and 1-D problems in order to solve the time-consuming problem of direct transport calculation. The method of characteristics (MOC) is usually used in radial 2-D transport calculation in order to capture radial complex geometry. The discrete ordinate (SN) method is selected as the axial 1-D transport sweeper in this work. The two solvers are coupled by transverse leakage terms. Therefore, the accuracy of 2-D/1-D method highly depends on the approximation of the transverse leakage term. For example, in KUCA benchmark test, the isotropic approximation will introduce more than 700 pcm errors to the eigenvalue since the angular correlation of the leakage term is ignored. However, the memory consumption of storing strictly angle related leakage terms is too large. In this work, an alternative method is proposed. The Fourier series expansion is used to approximate the leakage terms, while only a few moments need to be stored. Several benchmark problems have been tested to verify the accuracy of the Fourier-series-based transverse leakage terms. The results show that the improved leakage term can significantly improve the accuracy of eigenvalue with relatively low memory consumption.