In this article, a reduced-order H-infinity filter is designed for a delta operator system over multiple frequency intervals. By nonsmooth optimization techniques, subdifferential analysis is generalized in delta domain for minimizing the maximum value of the H-infinity performance over the multiple frequency intervals. Based on the subdifferential analysis, an efficient descent algorithm is developed to obtain the reduced-order H-infinity filter. Compared with some existing algorithms, the proposed descent algorithm not only reduces computational complexities but also improves the H-infinity performance. Numerical examples are presented to demonstrate effectiveness of the proposed descent algorithm.