In this paper a biharmonic problem with Navier boundary condition involving nearly critical growth is considered: △2=u(n+4)/(n-4)-ru > 0 inΩ and u=△u=0 on ∂Ω, where iΩs a bounded smooth convex domain in Rn(n≥5) and r > 0 is small. We show that any sequence of positive solutions with r→0 has to blow up and concentrate at finitely many points in the interior of the domain ω. With blow-up argument, we also give the energy a priori estimate of positive solutions.