We investigate the spectral characteristics of Lg wave using 346 waveforms recorded at 24 seismic stations located across Karakoram Fault (KKF) in western Tibet. The tectonic structure of western Tibet is very complex and formed of several blocks, which are separated by distinct suture zones. It is predominated by KKF which is one of the major strike-slip faults in western Tibet. To understand the spatial variation in crustal properties, we subdivide the study region into two parts across the KKF. The analysis of the decay of the spectral amplitudes of Lg waves with epicentral distances allows for the evaluation of the crustal quality factor Q_Lg, which is a direct measurement of attenuation. We have observed a frequency-dependent Q_Lg with strong attenuation in the crust though no variation is observed across the KKF. This is consistent with the reported body wave attenuation study for this region. The corner frequency (f_c) is observed to decrease linearly with distance in both sides of the KKF with an effective shift of 2.5 to 1 Hz at 400 km and 1 to 0.7 Hz near 1000 km respectively. The moment magnitude of each earthquake is computed using displacement spectrum and subsequently compared with the reported magnitude.