Based　on　the　generalized　inference　idea,　a　new　kind　of　generalized　confidence　intervals　is　derived　for　the　among-group　variance　component　in　the　heteroscedastic　one-way　random　effects　model.　We　construct　structure　equations　of　all　variance　components　in　the　model　based　on　their　minimal　sufficient　statistics;　meanwhile,　the　fiducial　generalized　pivotal　quantity　(FGPQ)　can　be　obtained　through　solving　an　implicit　equation　of　the　parameter　of　interest.　Then,　the　confidence　interval　is　derived　naturally　from　the　FGPQ.　Simulation　results　demonstrate　that　the　new　procedure　performs　very　well　in　terms　of　both　empirical　coverage　probability　and　average　interval　length.