A periodic micro-structure on optical microfibers induced by Plateau-Rayleigh instability (PRI) was investigated and a potential application for long period gratings (LPGs) fabrication was given. The linear relation between the average periods of micro-structures and the diameters of optical microfibers was demonstrated first. By brushing a glass rod with a Teflon droplet suspended at the end tip along microfibers, a continuous film of Teflon was formed at once, then the film broke up into a series of periodic droplets due to PRI. Periodic Teflon nodes were left after the evaporation of the solvent. A LPG structure based on polymer was finally formed by this method on a microfiber with a diameter of 5.5 μm. An attenuation transmission dip of 15 dB around 1447 nm was achieved. Investigation of the strain and temperature response characteristics of the grating presented a strain sensitivity of -2.5 pm/με and a temperature sensitivity of -157 pm/°C. The technique proposed here provides a versatile technique for polymer-based LPGs fabrication. Benefiting from the high sensitivities, LPGs based on numerous polymers fabricated in this way could have potential applications in optical and biological sensing.