In this paper, we demonstrated stable continuous-wave passively mode-locked operation of an Er:Lu2O3 laser at 3 µm, utilizing a semiconductor saturable absorber mirror (SESAM). By operating the laser in a dry nitrogen environment and utilizing a thermoelectric cooler (TEC) temperature control device to mitigate the thermal effects of Er:Lu2O3 and enhance laser stability, we further compensated for group delay dispersion within the laser cavity through chirped mirrors, an shortest pulse duration of 12.0 ps at a average output power of 150 mW was achieved, which occurred at a center wavelength of 2844 nm, and a pulse repetition rate of 83.5 MHz. Additionally, we achieved a maximum continuous-wave mode-locked output power of 213 mW at an absorbed pump power of 8.3 W, equivalent to a pulse energy of 1.3 nJ. The RF spectrum analysis of the pulse train indicated a high SNR of nearly 70 dB, signifying excellent stability. To the best of our knowledge, This is the first report on the realization of an ultrashort pulse width mode-locked Er:Lu2O3 laser in the mid-infrared band.