Energy transfer direction in $Er^{3+}-Tm^{3+}$-codoped fluorozirconate glasses has been studied. For $Er^{3+}-Tm^{3+}$-codoped glasses, the dependence of the green emission intensity on the pump power (Pex) of 800 nm has ranged from (Pex)$^2$ to (Pex)$^3$. From this multistep absorption, a 1.48 $mu m$ emission from the $^3F_4{ ightarrow}^3H_4$ transition on Tm$^{3+}$ ion has been found to transfer into $^4I_{13/2}$, $^4I_{9/2}$ and $^4S_{3/2}$ on $Er^{3+}$ ion. In case of the 1.06 $mu m$ pumping, the emissin ratio of $^3H_4$ level in $Tm^{3+}$ to $^4I_{13/2}$ in $Er^{3+}$ showed that the amount of the energy transfer from $Tm^{3+}$ into $Er^{3+}$ increased with the increasing concentration of $Tm^{3+}$ ion. Our two kinds of pumping scheme suggest that the direction of dominant energy transfer between $Er^{3+}$ and $Tm^{3+}$ should be dependent on whether the $^3F_4$ level resonates in $Tm^{3+}$ the level or not.