An autostereoscopic display system with a bicylindrical lens based on temporal-spatial multiplexing technique is introduced in this paper. The system comprises a directional scanning backlight, a liquid crystal display panel with high refreshing rate, and an eye tracking device. The directional scanning backlight consists of an LED board, two lenticular lens arrays with matching periods, a parallax barrier film, and other optical films. One of the lenticular lenses is a bicylindrical lens designed to reduce aberration, hence achieving better image quality. A prototype is set up based on the proposed structure. A series of experiments are conducted, and the overall performance of the prototype is evaluated. The LEDs are divided into 10 groups that form 10 view zones. On the one hand, it achieves full resolution in both 2D and 3D display modes. On the other hand, the viewing angle is increased to $\pm 26\mathrm{deg}$. Most importantly, the crosstalk is low. The minimum crosstalk is 6%, and the maximum crosstalk is 8.8% at a viewing angle of $\pm 22\mathrm{deg}$.