In this work, we have used the Friedmann equation of general relativity with quantum correction terms to the Newtonian potential to obtain the modified Friedmann equation with quantum correction. The behavior of the solution is examined with a sign of the correction being put into consideration. With the correction, the singular and non-singular universe is clearly spelled out. The results reveal that the quantum correction effect depends on the sign in the correction. Applying cosmological constant to the modified Friedmann Equation, we found out that the scale factor of the universe is given by the first order in the expression of We also compare the Friedmann Equations with Loop Quantum Gravity (LQG) to the Friedmann Equation with quantum correction and found out that, for negative the critical density is not feasible but it is feasible for positive values . Keywords: Cosmology, quantum cosmology, Cosmological constant, Quantum bounce, Radiation universe, Dust universe.
