Power electronics technology has been widely used for decades in the modern motor drive systems. Beyond the control flexibility, the power electronics devices (e.g., diode rectifiers) are also the main harmonic source to the grid due to their nonlinearity, which deteriorate the power grid quality and may cause unnecessary losses in power system transformers. Both degradations are apt to occur in motor drive applications. As a consequence, it calls for advanced and intelligent control strategies for the power electronics based drive systems like adjustable speed drives in industry. At present, many industrial drives are still equipped with three-phase diode rectifiers. Thus, it is difficult to implement the prior-art harmonic control strategies for active front-ends. Moreover, the total cost and complexity has become an obstacle for these harmonic elimination approaches in multiple drive systems. Therefore, in this paper, a new cost-effective harmonic mitigation approach has been proposed for multiple drives. The proposed approach can control the generated current harmonics by benefiting of the nonlinearity of the drive units and through a novel current modulation scheme. Simulation and experimental results have validated the effectiveness of the proposed approach in terms of harmonic elimination in three-phase multi-drive systems.