The recent commercial success of flexible and foldable displays has resulted in growing interest in stretchable electronics which are considered to be the next generation of the optoelectronic technology. Stretchable display technologies are being intensively studied for versatile applications including wearable, attachable, and shape changeable electronics. In this paper, we present high fill factor, stretchable inorganic light-emitting diode (LED) displays fabricated by connecting mini-LEDs and stretchable interconnects in a double-layer modular design. The double-layer modular design enables an increased areal coverage of LEDs and stretchable interconnectors with both electrical and mechanical stability. The main features of the double-layer modular design, fabrication processes, and device characteristics for the high fill factor, stretchable inorganic LED display are discussed, with experimental and computational results. Demonstrations of a passive matrix LED display confirm the potential value of the multi-layer structured, stretchable electronics in a wide range of applications that need high fill factor with high stretchability.