We study a block type 3D printer that performs assembly of toy block from 3D CAD models. In this system, a 3D CAD model is automatically converted to a block model consisting of primitive shapes of toy blocks. Then a feasible assembly plan of the block model is also generated automatically. According to the assembly plan, an industrial robot assembles a block sculpture layer by layer from bottom to top. This approach has advantages in terms of reusability of materials and easiness of combining multiple materials, which are difficult for conventional 3D printers. We introduce a technique to determine the order of block placement to assemble various patterns of block models reliably. The technique includes converting unassemblable shapes in the model to assemblable ones with support blocks and/or decomposition into subassemblies. In addition to this, we implement a robot control system to automatically generate a desired sculpture stably according to the determined placement order. Experiments of assembling toy block models are demonstrated. The results show that our system can assemble various block models.