Since 2008, China competitive sports have been rapidly developed. However, sports development cannot do without universities competitive physical education. China and America two countries are respectively world sports main country and world sports power, their competitive levels affect world sports competitive levels. The paper utilizes grey model, targeted at China and America two countries university competitive sports development status, it makes prediction. Regard America previous NCAA number of participants and number of participants’ changing rate as American universities competitive sports development evidence and take Chinese previous national university students’ athletics championships participants athletes and number of participants changing rate as Chinese universities competitive sports development evidence. With respect to this, it establishes four prediction models. The paper takes China previous national participants’ amount changing rate as examples, detailed discusses prediction process. Other three models are all using Matlab programming to calculate.