In this paper, a new design method considering a desired workspace and swing range of spherical joints of a DELTA robot is presented. The design is based on a new concept, which is the maximum inscribed workspace proposed in this paper. Firstly, the geometric description of the workspace for a DELTA robot is discussed, especially, the concept of the maximum inscribed workspace for the robot is proposed. The inscribed radius of the workspace on a workspace section is illustrated. As an applying example, a design result of the DELTA robot with a given workspace is presented and the reasonability is checked with the conditioning index. The results of the paper are very useful for the design and application of the parallel robot.