We present a simple modulation-free technique to stabilize a laser frequency to the Doppler-free spectra of an atomic vapor. Polarization spectroscopy with use of a balanced polarimeter allows us to obtain a background-free dispersion signal suitable for high-speed and robust frequency stabilization. We employed the method to the 5S(1/2) F = 2 --> 5P(3/2) F' = 3 transition of 87Rb atoms. The achieved feedback bandwidth was approximately 100 kHz, and an efficient suppression of the frequency noise in a laboratory environment was attained.