This paper discusses a feasibility of a new type of two-way system for single layer lattice domes with nodal eccentricity by investigating the dynamic behavior under earthquake motions. The proposed dome is composed of two main arches, intersecting each other with T-joint struts to provide space for tensioning membranes. The main purposes of this study are to calculate the nonlinear dynamic response under severe earthquake motions and to see the possibility of using this new type of two-way system for single layer lattice domes against earthquake motions. The results show that the main arches remain elastic except yielding of the joints of strut members that can be used to absorb some amount of strain energy at strong earthquake motion. Consequently, deformation of the main arches can be reduced and any heavy damages on the main arches can be minimized. A kind of damage-control characteristic appeared in this system may be utilized against severe earthquake motions, showing a possibility of designing a new type of single layer lattice dome.