He was one of the members of Iran national team in the first World Mind Sports Games held in Beijing (2008), in which the Iranian team surprisingly clinched the third place ahead of Hungary, USA and India.
Moradi in February 2016, became the second Iranian chess player to reach 2600 Elo after Ehsan Ghaem Maghami, and in the following month, he scored 2603 in his own personal record. In the same year, he won the Washington International tournament ahead of Gata Kamsky and Ilya Smirin.[4]
In 2022, Moradi shared 1st place in the 122nd U.S. Chess Open with Aleksey Sorokin with a score of 8/9 but lost in tie-breaks.[6] As Sorokin represents Russia, this qualified Moradi for the 2022 US Championship.