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A new algorithm is developed to accurately compute the electromagnetic (EM) fields in the layered biaxial anisotropic media. We enclose the computational region in an infinitely long rectangular region by four vertical truncation planes and establish the corresponding algorithm to approximate the EM fields in the entire space. The EM fields in this region are expanded as a two-dimensional (2-D) Fourier series of the transverse variables. By using the spectral state variable method, the generalized reflection coefficient matrices and transmission matrices are then derived to determine the Fourier coefficients per layer. Therefore, we can obtain the spatial-domain EM fields by summing the 2-D Fourier series. To enhance the accuracy and efficiency of this algorithm, we apply the method of images to estimate the influence of the artificial boundaries on the EM fields at the observer. We then further develop a quantitative principle to choose the proper size of the region according to the desired error tolerance. With the proper choice, the summation of the series can achieve satisfactory accuracy. This algorithm is finally applied to simulate the responses of the triaxial logging tool in transversely isotropic and biaxial anisotropic media and is verified through comparisons to the other method.