武威市
It is not known when Jia Su was born, but it is known that his family was from Henan Municipality (河南, i.e., the region of the Tang Dynasty eastern capital Luoyang). His family was originally from Guzang (姑臧, in modern Wuwei, Gansu). His grandfather's name was Jia Zhou (), and his father's name was Jia Ning (), and neither was listed with an office in the table of the chancellors' family trees in the "New Book of Tang", suggesting that they were commoners. Jia Su had at least one older brother, Jia Song ().