In this report, it is demonstrated that the generation of THz band-width longitudinal coherent acoustic phonons (CAPs) that propagate perpendicularly to graphene's basal plane can be achieved by photo-excitation of supported monolayer graphene. Through exclusively exciting graphene with femtosecond lasers, the observation of backward Brillouin oscillations showed that after graphene absorbed the 800nm light, longitudinal CAPs with momentum in the out-of-plane direction were generated. With the assist of a piezoelectric InGaN quantum well buried inside a wurtzite GaN substrate, the full spectrum of the CAPs was revealed. Experimental results showed that the longitudinal CAP pulse had a bipolar shape and its spectrum had reached up to 1THz. In attempt to understand the generation mechanism of the longitudinal CAP pulse, we proposed a hypothesis based on graphene's carrier dynamics.