  Electronic structure and magnetic properties of ZrFe$_2$ with a cubic Laves
phase are investigated by calculations based on the density functional theory.
The total magnetic moment (m) of 3.14 $\mu_B$ per formula unit (\emph{f.u.}) is
obtained at the experimental lattice constant (7.06 \AA), which is larger than
3.06 $\mu_B$/\emph{f.u.} obtained at the theoretical equilibrium lattice
constant (6.85 \AA). The localized $3d$ magnetic moment is in negative
diffusive sp background moment. We predict a two-step magnetic collapse under
pressure: one is from 3.06 $\mu_B$/\emph{f.u.} to 1.26 $\mu_B$/\emph{f.u.} at
about 3.6 GPa, and the other is from 0.5 $\mu_B$/\emph{f.u.} to nonmagnetic
state at about 15 GPa. We understand this process by the changes of density of
states. The magnetic moment decreases under the pressure in the vicinity of the
experimental lattice constant with $d\ln m/dp=-0.038$ GPa$^{-1}$. The
spontaneous volume magnetostriction is 0.015. We suggest that the Invar effect
of this alloy may be understood when considering the magnetic moment variation
according to the Weiss $2\gamma$-model.
