We apply $H(\cdot,\cdot)-\eta$-cocoercive operator introduced in [2] for solving a system of generalized variational-like inclusions in $q$-uniformly smooth Banach spaces. By using the approach of resolvent operator associated with $H(\cdot,\cdot)-\eta$-cocoercive operator, an iterative algorithm for solving a system of generalized variational-like inclusions is constructed. We prove the existence of solutions of system of generalized variational-like inclusions and convergence of iterative sequences generated by the algorithm. An example through Matlab programming is constructed.