This　paper　studies　the　problem　of　switching　H2　filter　design　for　linear　parameter　varying　(LPV)　systems　via　multiple　parameter-dependent　Lyapunov　functions.　Less　conservative　conditions　are　obtained　when　considering　the　hysteresis　switching　compared　with　the　existing　techniques,　the　design　problem　is　finally　formulated　into　linear　matrix　inequality　(LMI)　which　can　be　computed　efficiently　with　LMI　Control　Toolbox.　A　numerical　example　is　given　to　illustrate　the　effectiveness　of　the　proposed　method.