The excitation of high-order Laguerre-Gaussian mode in a Nd:YAG laser resonator was presented by applying the diffraction of a second-order circular Dammann grating (CDG) for annular pumping. In the study, the 808-nm pump light was shaped into double-ring structure by the CDG and matched spatially with that of an ideal LG11 mode. As a result, the laser resonator generated LG11 vortex mode, and the laser power reached 204 mW with 14.5-% slope efficiency. Also, when the cavity mirror was tilted, the laser output could switch to LG01 vortex mode. The results showed the convenience and versatility of CDG in annular-pumped vortex laser.