We present for the first time a theoretical model of Er 3+ -Tm 3+ -Pr 3+ codoped fiber pumped with both 800 nm and 980 nm lasers to explore possibility of this co-doped system as all-wave fiber amplifier. The rate and power propagation equations of the model are solved numerically and the dependence of the gains at 1310, 1470, 1530, 1600, 1650 nm windows on fiber length is calculated. The results show that with pump power of 200 mW/200 mW, when the concentrations of Pr 3+ , Tm 3+ , Er 3+ are around 1.7 × 10 24 , 3.9 × 10 24 , 1.2 × 10 24 (ions/m 3 ), respectively, the signals at 1310, 1470, 1530, 1600, 1650 nm may be nearly equally amplified with gain of 13-16.0 dB in the active fiber with length of 23.5 m; the co-doping concentrations and fiber length and pump powers may be further optimized to reduce the ripple.