Every point mass attracts every single other point mass by a force pointing along the lineintersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them
,
Where:
F is the force between the masses,
G is the gravitational constant,
m1 is the first mass,
m2 is the second mass, and
R is the distance between the masses.
On the other hand
When two bodies of different mass falls under vacuum condition they will fall at same time on the ground. That means that the gravitational force acting on these two bodies is same.

Now my question is that
According to Newton's law of gravitation the gravitational force acting on the body is directly proportional to the product of masses of the two bodies then, why didn't the body having more mass than the other falls earlier than the other which is having lighter mass then the first?

The FORCE on the bodies are different.

But what about the acceleration? Remember F = ma

And since the heavier mass object has a higher mass, the acceleration will be in such a way as to equal that of the lighter mass.

Because their acceleration is indeed equal! The gravitational field strength on both objects is the same:

g = \frac{GM}{r^2}

and does not depend on the mass of the other object, but only that of the Earth.