The thermal relaxation time for a chemically non-equilibrated gluon pl
asma is calculated using the non-equilibrium Debye mass as the infrare
d regulator. The dependence of the thermal relaxation time on the fuga
city is given. We find that there is a threshold fugacity lambda(g).
When lambda(g) < lambda(g), tau(NEQ)/tau(EQ) decreases sharply with i
ncreasing fugacity, while lambda(g) > lambda(g), the ratio is almost
unchanged. PACS: 24.85.+p, 12.38.Mh, 52.25.Dg.