This paper is concerned with the higher-dimensional haptotactic system modeling oncolytic virotherapy, which was initially proposed by Alzahrani–Eftimie–Trucu [Multiscale modelling of cancer response to oncolytic viral therapy, Math. Biosci. 310 (2019) 76–95] (see also the survey Bellomo–Outada et al. [Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision, Math. Models Methods Appl. Sci. 32 (2022) 713–792]) to model the process of oncolytic viral therapy. We consider this problem in a bounded domain Ω⊆ℝN(N=2,3) with zero-flux boundary conditions. Although the L∞-norm of the extracellular matrix density v is easily obtainable, the remodeling process still causes difficulty due to the deficiency of regularity for v. Relying on some Lp-estimate techniques, in this paper, under the mild condition on parameters, we finally established the existence of global-in-time classical solution, which is bounded uniformly. Moreover, the large time behavior of solutions to the problem is also investigated. Specially speaking, when κu=0, the corresponding solution of the system decays to (0,0,0) algebraically. To the best of our knowledge, these are the first results on boundedness and asymptotic behavior of the system in three-dimensional space.