Sequential quadratic programming (SQP) algorithms are widely recognized to be among the most successful algorithms for general constrained optimization. This paper attempts to develop an SQP-based method for equiripple FIR filters with low group delay. We explain how the complimentarily conditions in an SQP design algorithm help reduce the amount of computation required to update the Lagrange multipliers in a significant manner. Design examples are presented to illustrate the algorithm's performance that compares favorably with several existing design methods.