The application of microfluidic technology to manipulate cells or biological particles is becoming one of the rapidly growing areas, and various microarray trapping devices have recently been designed for high throughput single-cell analysis and manipulation. In this paper, we design a double-slit microfluidic chip for hydrodynamic cell trapping at the single-cell level, which maintains a high capture ability. The geometric effects on flow behaviour are investigated in detail for optimizing chip architecture, including the flow velocity, the fluid pressure, and the equivalent stress of cells. Based on the geometrical parameters optimized, the double-slit chip enhances the capture of HeLa cells and the drug experiment verifies the feasibility of the drug delivery.