Based on the multiconfiguration Dirac-Fock method, a new program was developed for the calculation of cross sections of dielectronic recombination (DR). As an example, the decay rates and the corresponding DR cross sections have been systematically calculated for the doubly excited state 1s2l2l′ of C3+, Ar15+, Kr33+ and U89+ ions. For C4+, Ar16+ and Kr34+ ions, a good agreement has been found between the present calculations and the previous theoretical and experimental results; for U90+ ion, the effect of the Breit interation on the DR cross sections has been emphasized especially.