In a color facsimile apparatus, a plurality of image data are grouped for each destination, and the groups are further sub-grouped on the basis of data types such as color and monochrome images. In addition, these groups may be sub-grouped on the basis of encoding types such as MR encoding and JBIG encoding. Each sub-group created in this manner includes a plurality of image data having the same destination and data type. Image data are transmitted on a sub-group basis. That is, a plurality of image data can be transmitted by originating a single call. Since only image data of the same type are transmitted with a single call, confusion on the receiving side can be prevented.