In a cylinder lock assembly, a latch operating tube has an enlarged end portion extending into an outer drive tube disposed in an outer handle. A locking spindle is disposed in the latch operating tube and has a locking tongue extending radially and outwardly through the outer drive tube to interlock with an outer rose when the locking spindle is pressed by a push button to move to a locked state. A locking plate is sleeved around the locking spindle and has a radial locking part to engage a protrusion that projects radially and inwardly from an inner surface of the enlarged end portion so that the locking spindle is locked against movements to an unlocked state when the locking spindle is in its locked state.