This　paper　investigates　the　problem　of　output　feedback　l(2)　-　l(infinity)　control　for　networked　system　with　random　delays.　The　sensor-to-controller　and　controller-to-actuator　delays　are　simultaneously　considered　due　to　limited　bandwidth　communication.　The　random　delays　are　described　by　a　binary　switching　sequence　satisfying　a　Bernoulli　distribution.　The　purpose　is　the　design　of　a　dynamic　output　feedback　controller　which　ensures　the　exponentially　mean-square　stability　of　the　closed-loop　system　and　guarantees　an　l(2)　-　l(infinity)　norm　bound　constraint　on　disturbance　attenuation.　Via　matrix　inequalities　a　sufficient　condition　for　solvability　of　this　problem　is　presented.　The　sequentially　linear　programming　method　(SLPMM)　is　applied　to　solve　the　matrix　inequalities.　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.