Since variable fractional delay （VFD） filter contains a large number of coefficients to be solved， this paper presents a study on sparse-constrained Farrow structure variable fractional delay filter. We add a L₁ regularization constraint to further enhance the sparsity based on coefficient symmetry and optimize its frequency response to approximate a desired frequency response in the minimax error sense. In addition， the alternating direction method of multipliers （ADMM） algorithm is used to iteratively obtain the filter coefficients. Simulation experiments demonstrate that the proposed sparse-constrained VFD filter not only ensures high delay accuracy but also reduces the use of multipliers and adders by 47.69% and 58.60% respectively， thus lowering system computation and complexity greatly.