A　multiobjective　filtering　problem　is　investigated　for　a　class　of　continuous-time　time-delay　systems　with　nonzero　initial　conditions.　The　plant　is　supposed　to　have　nonlinear　dynamics　and　multiple　time　delays　in　both　the　state　and　the　measured　output.　In　order　to　address　the　compatible　mixed　H-2　and　H-infinity　performance　measure　for　the　filtering　problem,　the　generalized　H-infinity　performance　index　is　introduced　instead　of　the　standard　one.　The　novel　mixed　H-2　and　H-infinity　filtering　problem　is　formulated　as　an　optimization　problem,　where　the　solvability　conditions　are　provided　via　convex　computation　approaches.　After　some　algebraic　transformations　and　decompositions,　the　involved　nonlinear　constraints　can　be　eliminated　and　linear　matrix　inequality-based　convex　algorithms　can　be　given　for　the　filter　design.　A　simple　example　is　given　to　illustrate　the　optimization　algorithms.