We present a 2.5-D finite difference (FD) algorithm to simulate the logging-while-drilling (LWD) electromagnetic (EM) measurements with arbitrarily oriented magnetic dipole sources in 2-D anisotropic media. The real 3-D modeling in the spatial domain is converted to a series of independent 2-D equations in the spectral domain by implementing the Fourier transform (FT). By replacing the dipoles with incident fields, the scattered fields are solved directly to avoid the point source singularity as well as improve the convergence of inverse FT (IFT). The efficiency of the IFT is further enhanced with a modified Gauss-Hermite (GHM) quadrature-based numerical integration scheme. Numerical tests demonstrate that the proposed 2.5-D algorithm is fast and accurate in modeling the LWD EM measurements in complex scenarios. Discussions are also made to compare the performance of the proposed methods with 1-D and 3-D algorithms.