When is the only time that an object has no gravitational potential energy

The gravitation potential energy of an object will be zero when it will be at ground.

Explanation:

The energy of an object due to its position is known as gravitational potential energy. Mathematically, it can be written as:

                                        P.E = mgh          ………… (i)

Equation (i) shows that P.E depends upon weight and height of the object above the ground. If h = 0 then,  

                                         P.E = mg(0)

                                           P.E = 0  

Hence, when the object will be at ground, its potential energy will be zero.