This paper studies an Erdélyi-Kober fractional coupled system where the variable is in an infinite interval, and the existence of positive solutions is considered. We first give proper conditions and then use the Guo-Krasnosel'skii fixed point theorem to discuss our problem in a special Banach space. The monotone iterative technique and the existence results of positive solutions for this system are established naturally. To show the plausibility of our main results, several concrete examples are given at the end.