A high power 755 nm continuous-wave (CW) laser with high beam quality based on the Alexandrite crystal was demonstrated. The Alexandrite lasers single-end-pumped by 638 nm laser diodes (LDs) and 532 nm solid-state laser were studied comparatively, then the CW output power, optical-to-optical conversion efficiency, and slope efficiency pumped by 638 nm LDs were 3.9 W, 19.7%, and 23.7%, respectively, while they were 2.1 W, 10.0%, and 12.9%, at nearly the same conditions except that it was pumped by 532 nm solid-state laser. The results show that the Alexandrite laser pumped with 638 nm LDs can obtain higher CW output power and higher conversion efficiency. Moreover, a CW output power of 6.2 W at 755 nm of Alexandrite laser double-end-pumped by a 638 nm LDs was achieved with the optical-to-optical conversion efficiency and the slope efficiency of 16.3% and 24.2%, respectively. The beam quality factor M2 was better than 1.47 at the CW output power of 5.0 W, which was the highest CW output power of Alexandrite laser with the diffraction limit to the best. This high power and high beam quality 755 nm Alexandrite laser provides the fundamental frequency source for the development of CW ultraviolet lasers.