The relativistic nuclear recoil corrections to the energy of the 2p_3/2 state of hydrogen-like and the (1s)²2p_3/2 state of high-Z lithium-like atoms in all orders in alpha Z are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low Z the results of the calculation are in good agreement with the alpha Z-expansion results. It is found that the total nuclear recoil contribution to the energy of the (1s)²2p_3/2-(1s)²2s transition in lithium-like uranium constitutes -0.09 eV.