A new type of optical amplifier based on co-doping erbium in thulium doped fiber is proposed to realize S+C band gain by dual-wavelength (800+1410 nm) pumping scheme which is obtainable from laser diode. A novel model is established for the co-doped fiber considering the Er3+ to Tm3+ energy transfer process. Using appropriate fiber parameters and energy transfer parameters, the coupled rate equations are analyzed and solved; the concentrations of Er3+ and Tm3+ and fiber length were optimized to get more uniform gain. The results predicted that the S+C band gain can be achieved at the same time by co-doping erbium in thulium doped fluoride fiber.