Transversal oscillation of coronal loops that are interpreted as signatures of magneto hydrodynamics (MHD) waves are observed frequently in active region corona loops. The amplitude of this oscillation has been found to be strongly attenuated. The damping of transverse oscillation may be produced by the dissipation mechanism and the wake of the traveling disturbance. The damping of transversal loop oscillations with wake phenomena is not related to any dissipation mechanism. Also, these kinds of coronal loop oscillations are not related to the kink mode, although this mode can be occurred after the attenuation process by the energy of the wave packet deposited in the loop.  In this paper the excitation and damping of transversal coronal loop oscillations with wake of traveling wave packet is discussed in detail, both theoretically and observationally. Here, the transversal coronal loop oscillations is modeled with a one dimensional simple line-tied. The dynamics of the loop and the coronal is governed by the Klein–Gordon differential equation. A localized disturbance that can be generated by nearby flare produces a perturbation that undergoes dispersion as it propagates toward the loop. As a consequence, the amplitudes of oscillates decay with time roughly t-1/2 at the external cutoff frequency. These observed data on 2016-Dec-4 by Atmospheric Imaging Assembly (AIA) onboard Solar Dynamic Observatory (SDO) observations data, consisting of 560 images with an interval of 24 seconds in the 171 A0 pass band is analyzed for evidence of excitation and damping of transverse oscillations of coronal loop that is situated near a flare. In this analyzed signatures of transverse oscillations that are damped rapidly were found, with periods in the range of P=18.5-23.85 minutes. Furthermore, oscillation of loop segments attenuate with time roughly as t-α that average values of α for 4 different loops change form 0.65-0.80. The magnitude values of α are in good agreement with theoretical prediction for damping of transverse loop oscillations by wake of the traveling wave packet that can be considered responsible for the rapid damping of the observed oscillations.