  Motivated by an experimental finding that the successive phase transitions in
$\alpha$-Sr$_2$CrO$_4$ observed at ambient pressure ceases to exist under high
pressures, we carry out the density-functional-theory-based electronic
structure calculations and demonstrate that the reversal of the crystal-field
splitting reported previously is restored under high pressures, so that the
orbital degrees of freedom disappears, resulting in the single phase transition
that divides the system into high-temperature Mott insulating and
low-temperature antiferromagnetic insulating phases.
