An apparatus for conveying cut flowers is provide which comprises a conveyor assembly with opposite, cooperating endless belts for there between conveying the cut flowers in a vertical position. The conveyor assembly comprises at least first and second conveyor sections, wherein the first conveyor section has an input location intended for receiving a cut flower and an output location intended for transferring said cut flower to the second conveyor section. The vertical position of the output location can be changed for changing its vertical position, and thus also the vertical position of the cut flower, relative to the second conveyor section.