A high-power continuous-wave (CW) ultraviolet (UV) laser at 378 nm from an intracavity frequency-doubled Alexandrite laser has been demonstrated with 638 nm fiber-coupled laser diodes as the pump source. A maximum output power of 2.55 W was obtained, which is the highest power for CW frequency-doubled Alexandrite lasers, to the best of our knowledge, corresponding to the optical-to-optical conversion efficiency of 7.9% from 638 nm pump laser to 378 nm UV laser. The beam quality factors M2 were measured to be 2.19 and 2.47 in x and y directions at UV output power of 1 W, respectively.