The applicability of lenticular-lens-based autostereoscopic 3D display is limited due to its crosstalk and degradation of resolution. Autostereoscopic display with no crosstalk and full resolution is realized by designing a butterfly-shaped liquid crystal display shutter in a multi-directional backlight unit. And the calculation formulas of parameters of the directional backlight lenticular panel are derived theoretically. Furthermore, the multi-directional backlight unit parameters of a 55 in (1 in=2.54 cm) 4K model autostereoscopic 3D displayer are presented, and they are optimized by TracePro software. The simulation results show that the crosstalk of designed autostereoscopic display is less than 0.01% which can be approximate to zero, and it can be fully compatible with the existing glasses shutter switch 3D video images with no loss of resolution.