The former laser systems are complex to realize multiple transverse modes. Only the fundamental mode and low-order modes can be generated, and the high-order modes are hard to be generated. Furthermore, the changing process of one frequency restraining another in mode competition is hard to be observed. A novel synthetical demonstration system of laser principle is presented based on a cat-eye cavity laser and the frequency splitting technology. In the system, a cat-eye retroreflector is treated as the cavity mirror of a He-Ne laser. More than ten typical transverse modes including fundamental mode, low-order modes, and high-order modes can be generated by adjusting the distance between two lenses in the retroreflector. In addition, more experiments of fundamental laser characteristics, such as longitudinal mode, laser polarization, and lasing bandwidth, are also carried out. In the condition of fundamental transverse mode, with a quartz crystal plate put in the cavity, laser frequency splitting and frequency difference adjusting can be achieved. Based on it, the dynamic process of mode competition can be observed.