This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G'/G, 1/G)-expansion and (1/G')-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.