  We have studied the pressure effect on electronic structures and magnetic
orders of ternary iron selenide K$_{0.8}$Fe$_{1.6}$Se$_2$ by the
first-principles electronic structure calculations. At low pressure, the
compound is in the blocked checkerboard antiferromagnetic (AFM) semiconducting
phase, as observed by the neutron scatting measurements. Applying pressure
induces two phase transitions, first from the blocked checkerboard AFM
semiconducting phase to a collinear AFM metallic phase around 12 GPa, and then
to a non-magnetic metallic phase around 25 GPa, respectively. Our results help
to clarify the recent experimental measurements under pressure.
