This article considers the following higher-dimensional quasilinear parabolicparabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions {ut =▽· (D(u)▽u)-▽· (S(u)▽v) + f(u),x ∈ Ω,t ＞ 0vt =△v+w-v,x ∈ Ω,t ＞ 0,wt =u-w,x ∈ Ω,t ＞ 0,in a bounded domain Ω (∈) Rn(n ≥ 2) with smooth boundary (e)Ω,where the diffusion coefficient D(u) and the chemotactic sensitivity function S(u) are supposed to satisfy D(u) ≥ M1(u + 1)-α and S(u) ≤ M2(u + 1)β,respectively,where M1,M2 ＞ 0 and α,β ∈ R.Moreover,the logistic source f(u) is supposed to satisfy f(u) ≤ a-μuγ with μ ＞ 0,γ ≥ 1,and a ≥ 0.As α + 2β ＜ γ-1 + 2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.