Thin-film thickness measurement based on spectral phase method is limited by the magnitude of the nonlinear spectral phase. To increase the sensitivity, a swept-source interferometer with recirculating sample loop is developed to obtain an amplified spectral phase from the thin-film under measurement. The spectral phase of the complex reflectivity of the thin-film can be accumulated in multiple passages of the probing light to the thin-film. After removing the linear spectral phase from the retrieved spectral phase, amplified nonlinear spectral phase corresponding to the thin-film is obtained. Using this amplified nonlinear spectral phase in a fitting model, the thin-film thickness can be determined with an enhanced precision.