  We propose an extrapolation method utilizing energy variance in the Monte
Carlo shell model in order to estimate the energy eigenvalue and observables
accurately. We derive a formula for the energy variance with deformed Slater
determinants, which enables us to calculate the energy variance efficiently.
The feasibility of the method is demonstrated for the full $pf$-shell
calculation of $^{56}$Ni, and the applicability of the method to a system
beyond current limit of exact diagonalization is shown for the
$pf$+$g_{9/2}$-shell calculation of $^{64}$Ge.
