We prove the existence of a positive solution for the system of the following nonlinear biharmonic equations with Dirichlet boundary condition $${{Delta}^2u+c{Delta}u+av^+=s_1{phi}_1+{epsilon}_1h_1(x);in;{Omega},\{Delta}^2v+c{Delta}v+bu^+=s_2{phi}_1+{epsilon}_2h_2(x);in;{Omega},$$ where $u^+= max{u,0}$, $c{in}R$, $s{in}R$, ${Delta}^2$ denotes the biharmonic operator and ${phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{Delta}$ with Dirichlet boundary condition. Here ${epsilon}_1$, ${epsilon}_2$ are small numbers and $h_1(x)$, $h_2(x)$ are bounded.