The vibration-vibration energy exchange of $N_2(v=1)+O_2(v=0){ o}N_2(v=0)+O_2(v=1)$ has been investigated, in particular, at low temperatures. The energy exchange rate constants are calculated by use of the solution of the time-dependent Schrodinger equation with the interaction potential of the colliding molecule as a perturbation term. The predicted rate constants are significantly agree with a experimental values in the range of 295∼$90^{circ}K$. The consideration of the VV-VT coupling decreases the predicted pure VV energy exchange value by a factor of ∼2. When the collision frequency correction is introduced, the VV-VT rate constant is consistent with the observed value in the liquid phase. The consideration of the population of the rotational energy level increases the VV-VT value significantly.