A new relativistic Hartree-Fock approach with density-dependent $sigma$, $omega$, $rho$ and $pi$ meson-nucleon couplings for finite nuclei and nuclear matter is presented. Good description for finite nuclei and nuclear matter is achieved with a number of adjustable parameters comparable to that of the relativistic mean field approach. With the Fock terms, the contribution of the $pi$-meson is included and the description for the nucleon effective mass and its isospin and energy dependence is improved.