DNA tile-based assembly provides a promising bottom-up avenue to create designer two-dimensional (2D) and three-dimensional (3D) crystalline structures that may host guest molecules or nanoparticles to achieve novel functionalities. Herein, we introduce a new kind of DNA tiles (named layered-crossover tiles) that each consists of two or four pairs of layered crossovers to bridge DNA helices in two neighboring layers with precisely predetermined relative orientations. By providing proper matching rules for the sticky ends at the terminals, these layered-crossover tiles are able to assemble into 2D periodic lattices with precisely controlled angles ranging from 20 degrees to 80 degrees. The layered-crossover tile can be slightly modified and used to successfully assemble 3D lattice with dimensions of several hundred micrometers with tunable angles as well. These layered-crossover tiles significantly expand the toolbox of DNA nanotechnology to construct materials through bottom-up approaches.