Pulsar-like compact stars provide us a unique laboratory to explore properties of dense matter at supra-nuclear densities. One of the models for pulsar-like stars is that they are totally composed of "strangeons", and in this paper, we studied the pulsar glitches in a strangeon star model. Strangeon stars would be solidified during cooling, and the solid stars would be natural to have glitches as the result of starquakes. Based on the starquake model established before, we proposed that when the starquake occurs, the inner motion of the star which changes the moment of inertia and has impact on the glitch sizes, is divided into plastic flow and elastic motion. The plastic flow which is induced in the fractured part of the outer layer, would move tangentially to redistribute the matter of the star and would be hard to recover. The elastic motion, on the other hand, changes its shape and would recover significantly. Under this scenario, we could understand the behaviors of glitches without significant energy releasing, including the Crab and the Vela pulsars, in an uniform model. We derive the recovery coefficient as a function of glitch size, as well as the time interval between two successive glitches as the function of the released stress. Our results show consistency with observational data under reasonable ranges of parameters. The implications on the oblateness of the Crab and the Vela pulsars are discussed.