A stretchable display and a manufacturing method thereof are disclosed. The stretchable display includes a stretchable substrate including a flat part and a plurality of protrusions protruding above the flat part, a plurality of fixed light emitting devices, each fixed light emitting device being attached to an upper surface of a corresponding protrusion of the plurality of protrusions, a plurality of moving light emitting devices, the moving light emitting devices being positioned among the plurality of protrusions, and a plurality of connection wirings connecting among the plurality of fixed light emitting devices and the plurality of moving light emitting devices.