In this paper, we report the design and fabrication of a long-period waveguide grating (LPWG) in a polymer ridge waveguide, which has a benzocyclobutene (BCB) core and an epoxy cladding of the same width. We first apply an accurate perturbation theory to evaluate the phase-matching condition of the grating and derive simple analytical expressions to highlight the temperature dependence of the resonance wavelength. The possibility of achieving a polarization-independent resonance wavelength is also discussed. We next describe the fabrication of an LPWG in a BCB/epoxy ridge waveguide by a UV-writing technique using a KrF excimer laser and present the transmission spectra of the grating measured at different UV dosages. By controlling the waveguide width, we produce an LPWG with a resonance wavelength that is polarization insensitive at a specific temperature. The temperature dependence of the LPWG is also discussed. Our results provide a better understanding of the operation principle of LPWGs, which should facilitate the design of LPWG-based devices for various applications.