In　robust　control　problems,　how　to　elicit　and　utilize　the　uncertainty　information　is　the　key　in　achieving　a　good　robust　performance.　For　passive　uncertainties,　the　phase　bound　plays　a　fundamental　role.　For　nonpassive　uncertainties,　the　gain　bound　is　used　up　to　date.　The　former　leads　to　the　passivity　approach　and　the　later　to　the　small-gain　approach.　A　recently　developed　bounded　positive　real　model　succeeded　in　extracting　both　the　phase　and　the　gain　information　from　passive　uncertainties.　However,　it　is　still　not　known　how　to　model　the　phase　bound　of　a　nonpassive　uncertainty.　Aiming　at　achieving　an　even　higher　performance　for　nonpassive　uncertain　systems,　this　article　proposes　a　new　model　together　with　a　modeling　procedure　for　a　class　of　nonpassive　uncertainties.　This　model　well　captures　both　the　gain　and　the　phase　features　of　the　nonpassive　uncertainty.　Further,　a　numerically　tractable　design　method　is　developed　by　extending　the　passivity　method.　The　advantage　of　the　proposed　method　is　demonstrated　through　a　real-world　case　study.