The main work of this paper is to study the following competitive forage-predator model: (see model (1.3)), where the parameter $a_i,b_i,\chi_i>0(i=1,2), \tau,\mu>0$ and$\alpha,\beta>1, r\in(\bar{\Omega}\times[0,+\infty))\cap L^\infty(\Omega\times(0,\infty))$is a given nonnegative function,and$\tau,\alpha,\beta$ satisfies certain conditions,by applying the theory of Neumann thermal semigroups and some classical inequalities, it is proved that the model (under homogeneous Neumann boundary conditions) has a unique globally bounded classical solution.