Summary: We propose a new algorithm belonging to the family of the sparse-mode spectral method to simulate turbulent flows. In this method the number of Fourier modes \({\mathbf k}\) increases with \(k\) more slowly than \(k^{D-1}\) in dimension \(D\), while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burgers’ equation and two-dimensional incompressible MHD flows.