We report the development of cavity-enhanced laser absorption spectroscopy with continuous wavelength tuning using a dual-feedback locking scheme. A compact optical cavity of 8 cm is used for achieving an effective optical path of 80 m in a volume of only 10 ml. Compared to the traditional cavity-enhanced absorption spectrometers, our approach sweeps an absorption feature with a full width at half maximum (FWHM) of 420 MHz in 5 seconds, achieving a spectral resolution at MHz-level. We also introduce a novel method to easily and precisely calibrate the frequency tuning range. Our study proves the feasibility of conducting high-sensitivity, high-resolution and rapidly tunable absorption spectroscopy in an optical cavity.