This　paper　considers　estimation　of　a　functional　partially　quantile　regression　model　whose　parameters　include　the　infinite　dimensional　function　as　well　as　the　slope　parameters.　We　show　asymptotical　normality　of　the　estimator　of　the　finite　dimensional　parameter,　and　derive　the　rate　of　convergence　of　the　estimator　of　the　infinite　dimensional　slope　function.　In　addition,　we　show　the　rate　of　the　mean　squared　prediction　error　for　the　proposed　estimator.　A　simulation　study　is　provided　to　illustrate　the　numerical　performance　of　the　resulting　estimators.