Wrong! Mass which is measured in kilograms does not change no matter where you are; the only thing that changes is your weight that is measured in Newtons.
The weight of an object with mass m in a gravitational field with acceleration g is given by
P = m.g
On Earth g =~ 9.8 m/s^2
On the moon g is about 1/6 of the earth's; that's why you "weigh" less yet you always have the same mass