Relativistic theory of the nuclear recoil effect in highly charged Li-like ions is considered within the Breit approximation. The normal mass shift (NMS) and the relativistic NMS (RNMS) are calculated by perturbation theory to zeroth and first orders in the parameter 1/Z. The calculations are performed using the dual kinetic balance method with the basis functions constructed from B-splines. The results of the calculations are compared with the theoretical values obtained by other methods.