Abstract: In this paper, a two-dimensional compound Fourier series expansion (2D-CFS) is used to price the guaranteed minimum death benefits (2D-GMDB) influenced by two logarithmic assets. The main idea is to model the dynamic price process of risk asset (can be equity funds, or mutual funds) as the index Lévy process, which is combined with the density function of the remaining life to construct an auxiliary function, which satisfies specific conditions is expanded via a two-dimensional complex Fourier series. In the calculation of the series coeffcients, we mainly considers two forms of remaining lifetime density functions, namely combination-of-exponentials density and the piecewise constant forces of mortality assumption, and uses the characteristic index of the known logarithmic asset model to calculate the progression coeffcient. For the logarithmic asset model, we select the geometric Brownian motion (GBM) and jump diffusion process (Jump) to simulate the logarithmic asset process. In the numerical experiment section, we consider the pricing problem of the 2D-CFS method under the exchange option, the maximum option, the minimum option and the geometric option, and the results are compared with the two-dimensional cosine series expansion (2D-COS) method, showing that the 2D-CFS method is significantly better than the 2D-COS method in terms of convergence speed and calculation accuracy.