We present an analytic model for the local bias of dark matter halos in a LCDM universe. The model uses the halo mass density instead of the halo number density and is searched for various halo mass cuts, smoothing lengths, and redshift epoches. We find that, when the logarithmic density is used, the second-order polynomial can fit the numerical relation between the halo mass distribution and the underlying matter distribution extremely well. In this model the logarithm of the dark matter

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... y is expanded in terms of log halo mass density to the second order. The model remains excellent for all halo mass cuts (from M_cut=3×10^11 to 3×10^12h^-1M_), smoothing scales (from R=5h^-1Mpc to 50h^-1Mpc), and redshift ranges (from z=0 to 1.0) considered in this study. The stochastic term in the relation is found not entirely random, but a part of the term can be determined by the magnitude of the shear tensor.