False
The mass of the object is not dependent on gravity.
The mass of the object is just the quantity of matter contained in an object.
It is the weight of an object that is dependent on gravity. For example the gravity on the Moon surface is more less than that on the Earth, and so an object would weigh less on Moon than on Earth. In fact the weight on the Moon would approximately be 6 times less than on the Earth.
Hope this helps.