  In this paper, we study the following the coupled chemotaxis--haptotaxis
model with remodeling of non-diffusible attractant $$ \left\{\begin{array}{ll}
u_t = \Delta u-\chi\nabla\cdot(u\nabla v)- \xi\nabla\cdot(u\nabla w)+\mu u(1-
u-w), \displaystyle{v_t=\Delta v- v +u},\quad \displaystyle{w_t=- vw+\eta
w(1-u-w)},\quad \end{array}\right. $$ in a bounded smooth domain $\mathbb{R}^2$
with zero-flux boundary conditions, where $\chi$, $\xi$ and $\eta$ are positive
parameters. Under appropriate regularity assumptions on the initial data $(u_0,
v_0, w_0)$, by develops some $L^p$-estimate techniques, we prove the global
existence and uniqueness of classical solutions when $\mu>0$ (where $\mu$ is
the logistic growth rate of cancer cells). Here we use an approach based on
maximal Sobolev regularity and the variation-of-constants formula remove the
restrictions $\mu$ is sufficiently large, which required in \cite{PangPang1}.
