In 2011, Aulaskari and J. Rattya (Michgan Math. J. Vol. 60) has introduced the concept of Fi-normal meromorphic functions on the unit disc D, where the function Fi(r) : [0, 1] - (0,00) is smoothly increasing. They examined the class of meromorphic functions F on D satisfying F#(z) = O(Fi(|z|)), as |z| - 1-. In this paper, the authors study algebraic differential equation with solution Fi- normal meromorphic function.