In　this　technical　note,　an　H-2　approach　to　network-based　control　system　with　multiple　packet　dropouts　is　introduced.　The　communication　links　over　network　media　are　assumed　to　be　data-packet　dropouts.　Two　channel　packet　dropouts　are　simultaneously　considered　due　to　limited　communication　capacity　and　unreliable　communication　links.　One　is　measurement　channel　packet　dropouts　which　are　from　the　sensor　to　the　controller.　The　other　is　control　channel　packet　dropouts　which　are　from　the　controller　to　the　actuator.　Stochastic　variables　satisfying　the　Bernoulli　random　binary　distribution　are　utilized　to　model　the　random　multiple　packet　dropouts.　A　linear　matrix　inequality(LMI)-based　design　method　is　proposed　for　designing　observer-based　feedback　H-2　controller　to　guarantee　the　closed-loop　networked　control　system　to　be　asymptotically　mean-square　stable　and　preserve　a　guaranteed　H-2　performance.　Finally,　an　illustrative　example　is　provided　to　show　the　applicability　of　the　proposed　method.