The two-dimensional hexagonal Fourier transform is introduced to reduce the background anisotropy in the numerical calculations with periodic conditions. Comparing to traditional Fourier transform with cartesian mesh, the large-scale background anisotropy is significantly reduced under different energy spectra.In addition, the phenomenon of small-scale background anisotropy is found to berelated to the type of low-pass filter. Considering the standard deviation of second order velocity correlation function with fixed two-point distance, the scaling at smallscales is a result of Taylor expansion, while the scaling at large scales can be explained by using a simplified single-wave number analytical model. The hexagonal Fourier transform can be easily implemented by using fast Fourier transform (FFT) libraries,and is expected to be applied in future pseudo-spectral methods of two-dimensional and quasi-three-dimensional turbulent flows to minimize the background anisotropy