We give a partial answer to a question posed by C. Pugh and M. Shub in [PS2]. A partially hyperbolic diffeomorphism $f\in \mathit{Diff}^{2}(M)$ is accessible if every two points of M can be connected by a path which is piecewise in a stable or an unstable leaf. We prove that accessibility is open in $\mathit{Diff}^{2}(M)$ among the partially hyperbolic diffeomorphisms with one-dimensional center bundle.