Modelling of wave motion and propagation characteristics of waves is of great significant in chemical engineering. Waves are the major source of chemical actions in various real life applications. We apply an efficacious solver to give exact traveling wave solutions of the Hirota-maccari model. This solver introduces closed-form wave structures of the solutions. The traveling wave solutions are expressed by hyperbolic function solutions. These solutions may be applicable for some real life problems in chemical engineering, biological engineering, plasma physics and etc. Some two and three dimensional graphics are plotted for certain parameter values to describe the propagation of traveling wave solutions. Finally, it is pondered that the proposed approach can also be applied to another sort of complex models.