We present a numerical model of an ${\mathrm{Er}}^{\mathrm{3}+}\text{-}{\mathrm{Tm}}^{\mathrm{3}+}\text{-}{\mathrm{Pr}}^{\mathrm{3}+}$ codoped fiber amplifier pumped with an $800\mathrm{nm}$ laser for the first time to the best of our knowledge. The rate and power propagation equations are solved numerically, and the dependence of the gains at 1310, 1470, and $1530\mathrm{nm}$ windows on the active ion concentrations and fiber length are calculated. The results show that with pump power of $20\mathrm{mW}$ , when ${\mathrm{Pr}}^{\mathrm{3}+}\text{-}{\mathrm{Tm}}^{\mathrm{3}+}\text{-}{\mathrm{Er}}^{\mathrm{3}+}$ concentrations are around $2.0\times {10}^{24}$ , $2.0\times {10}^{24}$ , and $2.26\times {10}^{24}$ ( $\text{ions}/{\mathrm{m}}^3$ ), respectively, the signals at 1310, 1470, and $1530\mathrm{nm}$ windows may be equally amplified in the active fiber with a length of $1.3\mathrm{m}$ .