This paper is concerned with a tumor invasion system with chemotaxis effect in a bounded interval I ⊂ ℝ under the homogeneous Neumann boundary condition with non-negative initial data (u0,v0,w0, z0), where the diffusivity D and the sensitivity S are assumed to be non-negative and fulfill D(σ) ≥ (σ + 1)m, 0 ≤ S(σ) ≤ (σ +1)α (with some m,α ∈ ℝ). It is shown that if α < m + 2, then the system possesses a global-in-time bounded solution.