An image processing apparatus capable of performing a plurality of pieces of image processing including scan processing of a document in parallel with a scanner unit. In the scan processing, when the document is conveyed, the scanner unit receives a first instruction for setting a transfer rate and sets the transfer rate based on the first instruction, and when the image data is transferred, the scanner unit receives a second instruction for setting the transfer rate. When the transfer rate indicated by the first instruction and the transfer rate indicated by the second instruction are different, the image data is transmitted after changing the transfer rate, based on the second instruction. When the transfer rate indicated by the first instruction and the transfer rate indicated by the second instruction are identical, the image data is transmitted without changing the transfer rate set based on the first instruction.