In this paper, we obtained five kinds of new doubly-periodic solutions by using sinh-Gordon equation expansion method for nonlinear coupled scalar field equations which show physical significance and application value. In degeneration, we can obtain the new solitary wave solutions and trigonometric function solutions. The results showed that the equation has plenty of constructions of solutions, the physical phenomena of the physical model which the equation described, will be the object many physicists and mathematicians further explore.