A highly sensitive fiber-optic Fabry-Perot microcavity strain sensor is fabricated using single-mode fibers and a glass capillary tube; the fabricated strain sensor is demodulated using the non-scanning correlation demodulation method. The sensor is fabricated by penetrating two vertically cut single-mode fused silica fibers into a hollow core fused silica fiber and fixing the fibers to both ends of the hollow core fused silica fiber. Thus, the enhanced cavity length-strain sensitivity of the fiber-optic Fabry-Perot microcavity strain sensor is realized. The sensor has a cavity length with micron dimension. The non-scanning correlation demodulation method is used for demodulation based on varying cavity lengths. For a fiber-optic Fabry-Perot microcavity strain sensor with an initial cavity length of 30.129 μm and a hollow core capillary length of 40 mm, the cavity length-strain sensitivity reaches 14.08 nm/με and its linearity is up to 99.7%.