This　paper　considers　the　asymptotic　stabilization　for　a　class　of　second-order　autonomous　switched　linear　systems　by　means　of　the　geometric　properties　of　the　phase　plane.　For　the　case　of　two　subsystems　with　unstable　focus　equilibrium,　the　＇most　stabilizing＇　control　law　of　the　linear　time-invariant　system　is　designed,　and　a　necessary　and　sufficient　condition　for　asymptotic　stabilization　is　presented.　Numerical　examples　show　this　approach　is　efficient.　This　approach　can　also　be　used　to　other　second-order　switched　systems　with　different　equilibrium　types.