To generate optical vortex with multiple topological charges, a simple scheme based on the phase mask shaping technique is proposed and applied in a seeded free electron laser. With a tailored phase mask, an extreme-ultraviolet (EUV) vortex with multiple topological charges can be produced. To prove the feasibility of this method, an eight-step phase mask is designed to shape the seed laser. The simulation results demonstrate that 100-MW, fully coherent EUV vortex pulses with topological charge 2 can be generated based on the proposed technique. We have also demonstrated the possibility of generating higher topological charges by using a phase mask with more steps.
