This　paper　proposes　an　optimal　dynamic　supply　of　parking　permits　under　uncertainties　in　the　mixed　traffic　environment　of　regular　vehicles　(RVs)　and　autonomous　vehicles　(AVs).　The　uncertainties　from　queuing　delay　and　cruising-for-parking　time,　respectively,　are　derived　from　parking　permit　holders＇　unascertainable　early　arrival/late　departure　and　the　randomness　of　vehicle　speed　for　cruising-for-parking　users.　We　formulate　the　dynamic　system　optimum　as　a　stochastic　optimal　control　problem,　aiming　to　minimize　the　total　time　lost　for　all　parking　users.　On　this　basis,　we　express　the　optimality　condition　as　Hamilton-Jacobi-Bellman　equation　and　propose　an　optimal　control　strategy　for　dynamic　supply　of　parking　permits　(called　optimal　parking　supply　scheme).　The　proposed　scheme　is　determined　by　two　observable　and　measurable　variables,　i.e.,　queuing　time　and　cruising-for-parking　time.　We　find　that　the　scheme　can　significantly　reduce　the　total　system　time　lost,　especially　when　the　uncertainty　from　parking　permit　holders　is　at　a　high　level　or　the　percentage　of　AVs　is　small.　Finally,　a　case　study　of　a　selected　sample　area　in　Beijing　is　conducted,　which　verifies　the　efficiency　of　the　proposed　scheme　numerically.