Abstract This paper provides a comparison study on the homogenization methods based on asymptotic approach and fast Fourier transform (FFT), respectively. Their essential ideas, numerical implementation, efficiency, applicability as well as the deformation modes of unit cell are reviewed and compared. Numerical examples show that the effective mechanical properties obtained by FFT-based homogenization are smaller than those of asymptotic homogenization with the same mesh but within an acceptable error margin with a finer mesh. Because a conjugate gradient algorithm is used, the FFT-based homogenization method can obtain the results much faster than asymptotic homogenization which is based on finite element analysis. We find FFT-based can be used for porous structures with infinite contrast in Young’s modulus of solid material and void material. We propose an algorithm to calculate the node displacement of unit cell for FFT-based homogenization and note it can generate deformation patterns which came more reasonably reflect periodic boundary conditions than asymptotic homogenization.