In recent years, off-axis injection schemes based on nonlinear kicker magnets have emerged as a new research focus, particularly suitable for storage rings with small dynamic apertures. This scheme is characterized by a strong magnetic field generated by the nonlinear kicker magnet at the injection point to deflect the injected beam, while maintaining a near-zero magnetic field near the central orbit, significantly reducing interference with the stored beam. This paper presents the design of a nonlinear kicker magnet with an eight-conductor layout, conducting an in-depth study on the impact of key parameters—such as conductor layout, edge fields at the magnet ends, and ceramic vacuum coatings—on magnetic field performance, followed by optimization of these parameters. Results indicate that this nonlinear kicker magnet design meets the injection system requirements for the high-brightness electron-positron collider and synchrotron radiation ring under development.