  We propose an efficient and robust method to estimate the halo concentration
based on the first moment of the density distribution, which is $R_1\equiv
\int_0^{r_{\rm vir}}4\pi r^3\rho(r)dr/M_{\rm vir}/r_{\rm vir}$. We find that
$R_1$ has a monotonic relation with the concentration parameter of the NFW
profile, and that a cubic polynomial function can fit the relation with an
error $\lesssim 3\%$. Tests on ideal NFW halos show that the conventional NFW
profile fitting method and the $V_{\rm max}/V_{\rm vir}$ method produce biased
halo concentration estimation by $\approx 10\%$ and $\approx 30\%$,
respectively, for halos with 100 particles. In contrast, the systematic error
for our $R_1$ method is smaller than $0.5\%$ even for halos containing only 100
particles. Convergence tests on realistic halos in $N$-body simulations show
that the NFW profile fitting method underestimates the concentration parameter
for halos with $\lesssim 300$ particles by $\gtrsim 20\%$, while the error for
the $R_1$ method is $\lesssim 8\%$. We also show other applications of $R_1$,
including estimating $V_{\rm max}$ and the Einasto concentration $c_{\rm
e}\equiv r_{\rm vir}/r_{-2}$. The calculation of $R_1$ is efficient and robust,
and we recommend including it as one of the halo properties in halo catalogs of
cosmological simulations.
