By using the transforming operators, the Q-deformation of the nonharmonic o
scillator algebra is obtained. Based on the algebra, the Q-deformation of g
eneralized coherent states are introduced. It is found that these states ha
ve the overcompleteness and they are the minimal uncertainty states for the
Q-deformed natural operators, and the relative rate of squeezing of the Q-
deformation of generalized even coherent state increases with the degree of
deformation in the principal squeezing region.