1. An image processing apparatus comprising: at least one memory which stores data of each of at least Y image and Cb image or Cr image having no dependence upon each other's data; a memory access unit which reads out the data from and writes the data in said memory; and a filtering processing unit which receives the data read out by said memory access unit, performs a deblocking filtering process on the received data, and supplies the processed data to said memory access unit, wherein said filtering processing unit performs a deblocking filtering process on a block boundary of the Y image and a block boundary of the Cb image or Cr image alternately.