We achieve laser frequency stabilization by a simple technique based on sub-Doppler dichroic atomic vapor laser lock (DAVLL) in atomic cesium. The technique that combines saturated-absorption spectroscopy and Zeeman splitting of hyperfine structures allows us to obtain a modulation-free dispersion-like error signal for frequency stabilization. For the error signal, the dependence of peak-to-peak amplitude and the slope at the zero-crossing point on the magnetic field is studied by simulation and experiment. Based on the result, we obtain an available sub-Doppler DAVLL error signal with high sensitivity to the frequency drift by selecting an appropriate strength of the magnetic field. Ultimately, the fluctuation of the locked laser frequency is confined to below 0.5 MHz in a long term, exhibiting efficient suppression of frequency noise.