In designing left-handed metamaterials composed of magnetic resonators and electric resonators, two design principles, that is, the single-loop mirror-symmetry design principle and double-loop (quadruple-loop) mirror-symmetry design principle, were respectively proposed for the design of magnetic resonators and electric resonators. Based on the two principles, new structures with simultaneously negative permeability and permittivity were designed. By means of simulation experiments, the double-negative property of the proposed structure as well as the two design principles was verified. The two design principles and structures proposed in this paper are of great practical values in designing new types of left-handed metamaterials.