The interaction process between a nanosecond hyper-Gaussian laser pulse and a fullerene C60 molecular medium is studied by numerically solving the paraxial wave and particle rate equations through the hyper-Gaussian laser pulse Crank-Nicholson difference method. The evolution of the strong hyper-Gaussian laser pulse with different orders is simulated. Optical power limiting behavior caused by reverse saturable absorption is observed when the strong hyper-Gaussian pulse is propagating in the C60 molecular medium. The spatiotemporal shape of the hyper-Gaussian pulse can be obviously reshaped during propagation, and incident pulse with flat-topped time envelope distribution and central symmetry turns into the pulse with tip laser pulse distribution and asymmetry gradually. The pulse width decreases by an order of magnitude owing to the strong reverse saturable absorption of C60. Thus, the higher the order of the hyper-Gaussian pulse is, the more the reverse saturable absorption is, and the narrower the width of the output pulse is.