Sparse grid is one of Non-uniform grid forms with special properties of hierarchical interpolation. These is an algorithm of discrete Fourier transform on sparse grid, which is called Hyperbolic Cross FFT. This algorithm effectively reduce the number of sampling points, andminimize exponential time complexity of d-dimensions DFT algorithms to O(Nlog^dN). Hexagonal lattice is another kind of grid which has some special propertys such as number of sampling points less and higher sampling efficiency etc. This research focus on combining hexagonal lattice with sparse grid to design FFT algorithm on hexagonal sparse grid. We successfully achieve FFT algorithm on hexagonal sparse grid by defining ahexagon and square lattice conversion between subccript. And the new algorithm is proved to be effective by numerical experiments.