The continuous wave (CW) and passive mode-locking features of a diode-pumped Nd:CGA laser are experimentally demonstrated with a typical X-type cavity. Under the CW operation, different output couplers (OCs) were used to optimize the CW output power of the Nd:CGA laser. With the OC of 20% transmission, the maximum CW output power of 1.8 W is achieved and the slope efficiency is 30.8% at the central wavelength of 1079 nm. By employing a semiconductor saturable absorber mirror for passive mode-locking, pulses as short as 2.7 ps with 177 MHz repetition rate are achieved for OC with transmission of 1.6%. The maximum average output power of 524 mW is obtained under a pump power of 6.9 W. The optical-to-optical conversion efficiency and the slope efficiency are 7.6% and 8.0%, respectively.