By employing a new improved approximation scheme to deal with the centrifugal term and pseudo-centrifugal term, we solve approximately the Dirac equation with the hyperbolic potential for the arbitrary spin-orbit quantum number κ. Under the condition of the spin and pseudospin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.