Summary: This paper studies the parabolic-parabolic Keller-Segel system with supercritical sensitivity: \(u_{t}=\nabla\cdot(\phi (u) \nabla u)-\nabla \cdot(\varphi(u)\nabla v)\), \(v_{t}=\Delta v -v+u\), subject to homogeneous Neumann boundary conditions in a bounded and smooth domain \(\Omega\subset\mathbb{R}^n\)\((n\ge2)\), the diffusivity fulfills \(\phi(u)\ge a_0(u+1)^{\gamma}\) with \(\gamma\ge0\) and \(a_0>0\), while the chemotactic sensitivity satisfies \(0\le \varphi(u)\le b_0u(u+1)^{\alpha+\gamma-1}\) with \(\alpha>\frac{2}{n}\) and \(b_0>0\). It is proved that the problem possesses a globally bounded solution for \(\frac{4}{n+2}<\alpha<2\), whenever \(\|u_0\|_{L^{\frac{n\alpha}{2}}(\Omega)}\) and \(\|\nabla v_0\|_{L^{\frac{n\alpha+2\gamma}{2-\alpha}}(\Omega)}\) is sufficiently small. Similarly, the above conclusion still holds for \(\alpha>2\) provided that \(\|u_{0}\|_{L^{n\alpha-n}(\Omega)}\) and \(\|\nabla v_0\|_{L^{\infty}(\Omega)}\) are small enough.