As an innovative propulsion technique, laser augmented chemical propulsion (LACP) seems superior to the traditional ones. However, the corresponding combustion theories have still to be ascertained for LACP. Burning rate of 5-aminotetrazole (5-ATZ) propellant has been studied by testing pressed samples under different combustor pressures and laser powers. Based on micro computed tomography (MicroCT), an advanced thickness-over-time (TOT) method to characterize the regression of the produced non-planar burning surface is established. Because of a shell structure covering the combustion surface, the burning rate of the implemented 5-ATZ propellant is not constant during laser ablation. Resorting to functional fitting, a new law of non-constant burning including the effect of the observed unique burning surface structures is proposed. Accordingly, applicable combustion conditions of 5-ATZ based propellants have been preliminarily speculated for future research activities.