A simple liquid crystal display (LCD) backlight unit (BLU) comprising only a single-sheet polydimethyl siloxane (PDMS) light-guide plate (LGP) has been developed. The PDMS LGP, having micropatterns with an inverse-trapezoidal cross section, was fabricated by backside 3-D diffuser lithography followed by PDMS-to-PDMS replication. The fabricated BLU showed an average luminance of $2878\mathrm{cd}∕{\mathrm{m}}^2$ with 73.3% uniformity when mounted in a $5.08\mathrm{c}\mathrm{m}$ backlight module with four side view $0.85\mathrm{cd}$ LEDs. The developed BLU can greatly reduce the cost and thickness of LCDs, and it can be applied to flexible displays as a flexible light source due to the flexible characteristic of the PDMS itself.