By means of an optical fiber sensor based on beam deflection technique, the laser-induced plasma shock waves propagating in transparent organic glass are systemically investigated in experiments. Under the condition of free attenuation of shock wave, the temporal and spatial variations of some important parameters on the shock fronts are obtained by analyzing the experimental data. The experimental results reveal that shock waves, in the same medium, attenuate more slowly with the increase of laser energy; at the same time, propagation distance of shock waves increase when they have changed into sound waves.