By using the method simulated shells, the axisymmetrical non-linear dynamic equations of three-dimensional single-layer shallow conical lattice shells with equilateral triangle mesh are founded. Though the separating variables function method, a quadric and cubic non-linear differential equation is gotten by using Galerkin method. In order to study chaos movement, Accurate solution of non-linear free vibration differential equation is by solving a kind of free vibration equation of non-linear dynamics system. Critical Condition is gotten by using Melnikov function. Besides, numerical-graphic method also confirm the existence of chaos.