In frequency hopping communication system, the correlation characteristic of frequency hopping sequence is an important standard to measure the system performance. Therefore, the design of new frequency hopping sequences with low correlation property has always been one of the important topics in frequency hopping systems. In this paper, we present a class of frequency hopping sequences with respect to the Lempel-Greenberger bound, which is based on the character sums over finite fields and the decimation of m-sequences. The parameters of this frequency hopping sequences are new. Mathematics Subject Classification: 11B50, 11B65, 11B83.