We proposed and demonstrated a high power mode-locked fiber laser using a new type of gain medium which is called as Erbium Gallium co-doped fiber (Ga-EDF). The mode-locking mechanism is enabled by a graphene-based saturable absorber, which is fabricated by slotting a single layer graphene (SLG) thin film in between two fiber ferrules connected through an adaptor. The Ga-EDF has an absorption rate of 25 dB/m at 980 nm. With a 2-m-long Ga-EDF utilized as the primary gain medium in the laser system, the proposed laser can generate mode-locked solitons, with the central wavelength of 1560 nm, a 3 dB bandwidth of 3.20 nm and an average output power of 18.23 mW. The generated pulse yields a repetition rate of 12.25 MHz with pulse duration and pulse energy of 860 fs and 1.49 nJ respectively. For comparison purpose, the experiment is repeated by replacing the Ga-EDF in the laser cavity with the same length of 2-m-long conventional erbium-doped fiber (EDF), and similar measurement of the mode-locked output performance is undertaken. The result obtained shows in comparison an improvement of the mode-locked Ga-EDF laser output performance to that of the mode-locked EDF laser in terms of the 3 dB bandwidth, pulse width and signal-to-noise ratio. The proposed work is the first time, to the knowledge of the authors, that the application of Ga-EDF as an active gain medium in the development of mode-locked fiber laser incorporating graphene which is a thin layer film as a saturable absorber is explored.