When an object falls freely on the earth, the gravitational force acting on the body

The direction of acceleration will be the same as the force acting on the body. 

As we know, gravitational force will always attract and the direction of the force will always be towards the centre of another body. and 'g' is the acceleration due to gravitational force, so the direction of force/acceleration would be towards the centre of the earth. Also, the force will depend on the distance between the two bodies, so it is not constant.