Models of the dispersion-managed soliton system with third-order dispersion periodicity variaty are designed, their effects on dispersion-managed soliton propagation are investigated. The results show, time delay of soliton versus propagation distance will linearly arise mainly, and the effects independently exist. We can obtain the mean values of effects by third-order dispersion along propagation distance. The effect of third-order dispersion can be significantly suppressed if third-order dispersion of the fiber is periodically alternated between the positive and negative regimes.