To decide if the {sc parameterized feedback vertex set} problem

in directed graph is fixed-parameter tractable is a long standing

open problem. In this paper, we prove that the {sc parameterized

feedback vertex set} in directed graph is fixed-parameter

tractable and give the first FPT algorithm of running time

$O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set}

problem in directed graph can be transformed to a {sc

feedback vertex set} problem in directed graph,

hence we also show that the {sc parameterized feedback arc set}

problem can be solved in time of $O((1.48k)^kn^{O(1)})$.