We　consider　the　problem　of　variable　selection　for　the　fixed　effects　varying　coefficient　models.　A　variable　selection　procedure　is　developed　using　basis　function　approximations　and　group　nonconcave　penalized　functions,　and　the　fixed　effects　are　removed　using　the　proper　weight　matrices.　The　proposed　procedure　simultaneously　removes　the　fixed　individual　effects,　selects　the　significant　variables　and　estimates　the　nonzero　coefficient　functions.　With　appropriate　selection　of　the　tuning　parameters,　an　asymptotic　theory　for　the　resulting　estimates　is　established　under　suitable　conditions.　Simulation　studies　are　carried　out　to　assess　the　performance　of　our　proposed　method,　and　a　real　data　set　is　analyzed　for　further　illustration.