We have calculated the vibrational overtone dephasing rates of an oscillator that is subject to uncorrelated, impulsive, and strong collisions. We have assumed the Poisson statistics for binary collisions, and not truncated the cumulant expansion at the second order. The decay of the response function is always exponential, and the dephasing rate shows subquadratic dependence on the vibrational quantum number (nu). The dephasing rate asymptotically converges to the collision frequency at the large-nu or strong collision limits. We have succeeded in reproducing the experimental results on chloroform [K. Tominaga and K. Yoshihara, J. Phys. Chem. A 102, 4222 (1998)] and those on methyl iodide [A. B. Myers and F. Markel, Chem. Phys. 149, 21 (1990)] by adjusting the collision frequency and the strength of the collision.