We say that gravitational potential energy is zero when the object is on the ground(earth surface). My doubt is that can gravitational potential energy be considered zero anywhere (at any altitude) when object is kept on the surface of earth? And also there is distance between the object and the centre of the earth, how can the gravitational potential energy be considered zero?
Potential is never absolute, but always in relation to some reference. Earth being a common ground all over the world, it is natural choice for reference zero.
So all over the world, earth is always taken as zero potential. Anywhere on earth, or even in water, potential is same, and this also makes it ideal choice.