Apart from the IMO which is for the younger students, I am looking for competitions which are maybe for undergraduates or graduate students.
You can find all related information at the below link:
Undergraduate competitions which I know are:
International Mathematics Competition For University Students. The competition page is here.
The Consortium For Mathematics and its Applications sponsors contests one of which is international in the are of Mathematical Modeling: http://www.comap.com/undergraduate/contests/