Abstract: In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source: where k₁ e^pu≤D（u） or k₁ u^p≤D（u）;k₂ e^qu≤S（u）≤k₃ e^qu;g（u）≤a-be^ku.It is proved that,if q <k-1 or q=k-1 and b> b₀ for some constant b₀> 0,then there exists a unique classical solution which is globally bounded.The results show the effect of the aggregation and the logistic damping source on the existence of globally bounded solutions.

Key words: Chemotaxis, Nonlinear Diffusivity, Aggregation, Logistic Type Damping, Globally Bounded Solution