Abstract: Average Hamming correlation is an important performance indicator of frequency hopping sequences. Usually, the length of correlation window is shorter than the period of chosen frequency hopping sequence, so the study of partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the average partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the low hit zone, the average partial Hamming autocorrelation and the average partial Hamming crosscorrelation are established. It is shown that this new bound includes the known Peng-Peng-Tang-Niu bound for conventional frequency hopping sequences as special cases.