A good thermo-optic property of strontium dodeca-aluminum oxide (SrAl12O12, SRA) host material is very advantageous to the development of high-performance lasers by doping rare-earth ions for gain medium. In this work, we report on diode-end-pumped high-performance continuous-wave and passively Q-switched Nd:SRA lasers. For continuous-wave operation, a maximum output power of 6.45 W is achieved at 1049 nm with a slope efficiency of about 41.6%. Using a Y3Al5O12 (YAG) etalon, we have firstly achieved a 1066 nm laser with a maximum output power of 4.15 W and a slope efficiency of about 27%, to the best of our knowledge. For passively Q-switched operation, with Cr4+:YAG as a saturable absorber, a maximum average output power of 1.82 W was achieved with the shortest pulse width of 18.2 ns at pulse repetition rate of 22.9 kHz. The single-pulse energy and pulse peak power were 79.4 μJ and 4.3 kW. This work has further verified that the Nd:SRA crystal is very promising for high-performance laser generation.