In　this　article,　a　partially　linear　single-index　model　for　longitudinal　data　is　investigated.　The　generalized　penalized　spline　least　squares　estimates　of　the　unknown　parameters　are　suggested.　All　parameters　can　be　estimated　simultaneously　by　the　proposed　method　while　the　feature　of　longitudinal　data　is　considered.　The　existence,　strong　consistency　and　asymptotic　normality　of　the　estimators　are　proved　under　suitable　conditions.　A　simulation　study　is　conducted　to　investigate　the　finite　sample　performance　of　the　proposed　method.　Our　approach　can　also　be　used　to　study　the　pure　single-index　model　for　longitudinal　data.