Microfluidics has been the most promising platform for drug screening with a limited number of cells. However, convenient on-chip preparation of a wide range of drug concentrations remains a large challenge and has restricted wide acceptance of microfluidics in precision medicine. In this paper, we report a digital microfluidic system with an innovative control structure and chip design for on-chip drug dispensing to generate concentrations that span three to four orders of magnitude, enabling single drug or combinatorial multi-drug screening with simple electronic control. Specifically, we utilize droplet ejection from a drug drop sitting on a special electrode, named a drug dispenser, under high-voltage pulse actuation to deliver the desired amount of drugs to be picked up by a cell suspension drop driven by low-voltage sine wave actuation. Our proof-of-principle validation for this technique as a convenient single and multi-drug screening involved testing of the drug toxicity of two chemotherapeutics, cisplatin (Cis) and epirubicin (EP), towards MDA-MB-231 breast cancer cells and MCF-10A normal breast cells. The results are consistent with those screened based on traditional 96-well plates. These findings demonstrate the reliability of the drug screening system with an on-chip drug dispenser. This system with fewer cancer cells, less drug consumption, a small footprint, and high scalability with regard to concentration could pave the way for drug screening on biopsied primary tumor cells for precision medicine or any concentration-related research.