This paper is devoted to the Cauchy problem of the parabolic-parabolic Keller-Segel system with growth source and nonlinear secretion in any dimensional setting: \(u_t=\Delta u-\chi \nabla \cdot (u\nabla v )+f(u),v_t=\Delta v-\lambda v+g(u)\) , where \(\chi ,\lambda >0\) . The generalized logistic source f(u) satisfies \(0\le f(u)\le u(a-bu^{\gamma -1})\) with some \(a,b>0\) and \(\gamma >1\) ; the signal production term g(u) satisfies \(0\le g(u)\le \mu u^{k}\) with \(\mu ,k>0\) . We discuss the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial functions. Moreover, the solutions converging to positive constant equilibria is demonstrated for strictly positive initial data, building upon the persistence of classical solutions in the case of \(f(u)=u(a-bu^{\gamma -1}),\gamma \in (1,2)\) and \(g(u)=\mu u\) .
