A new laser cutting manipulator based on Delta parallel robot is proposed. Inverse equations and even the inverse kinematics model of the three-degree-of-freedom Delta parallel structure are established. The geometric shape of each subchain's workspace is analyzed and how the interior hole is formed are discussed in the test, so the problem of workspace depends on the solution of outside boundary and interior hole boundary of workspace. Using the combined method between geometric algorithm and numerical iterative algorithm, the geometric contour of each subchain's workspace is taken into account and the boundary conditions of all the workspace region are discussed thoroughly. Through above analysis, the whole solution process is intuitional and concise, and the calculation speed is even faster.