This study concerns the existence of positive solution for the following nonlinear boundary value problembegin{gather*}-Delta_{p(x)} u= a(x)h(u) + f(v) quadtext{in }Omega\-Delta_{q(x)} v=b(x)k(v) + g(u) quadtext{in }Omega\u=v= 0 quadtext{on } partial Omegaend{gather*}where $p(x),q(x) in C^1(mathbb{R}^N)$ are radial symmetric functions such that $sup|nabla p(x)| < infty,$ $sup|nabla q(x)|<infty$ and $1 < inf p(x) leq sup p(x) <infty,1 < inf q(x) leq sup q(x) < infty$, and where $-Delta_{p(x)} u = -mathop{rm div}|nabla u|^{p(x)-2}nabla u,-Delta_{q(x)} v =-mathop{rm div}|nabla v|^{q(x)-2}nabla v$ respectively are called $p(x)$-Laplacian and $q(x)$-Laplacian, $Omega = B(0 , R) = {x | |x| < R}$ is a bounded radial symmetric domain, where $R > 0$ is a sufficiently large constant. We discuss the existence of positive solution via sub-supersolutions without assuming sign conditions on $f(0)$ and $g(0)$.