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We propose and demonstrate a new method to control precisely the group velocity of slow surface plasmon polaritons propagating in a superlattice by changing incident pulsewidth. The validity of this method is confirmed by numerical simulations with the finite-difference time-domain. The group velocities for different frequency components are different. Therefore, for the Gaussian pulse, the group velocity is varied with the pulsewidth. Our method of control group velocity offers a new avenue for potential applications of the tunable slow surface plasmon polaritons.