Abstract This paper studies the chemotaxis–haptotaxis model of cancer invasion u t = Δ u − χ ∇ ⋅ ( u ∇ v ) − ξ ∇ ⋅ ( u ∇ w ) + μ u ( 1 − u − w ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , w t = − v w , x ∈ Ω , t > 0 in a bounded smooth domain Ω ⊂ R 3 with zero-flux boundary conditions, where the parameters χ , ξ and μ are positive. It is shown that the corresponding initial–boundary problem possesses a unique classical solution which is global in time and bounded under the explicit condition μ ≥ ( 11 2 + ξ 2 ‖ w 0 ‖ L ∞ ( Ω ) 2 ) χ 2 + 37 2 + 4 ξ 2 ‖ w 0 ‖ L ∞ ( Ω ) 2 and suitable regularity assumptions on the initial data ( u 0 , v 0 , w 0 ) .