According to Al-Kafeel website, it includes lessons on Tajweed recitation and Quranic sciences.
Sayed Muhnad al-Mayali, who is in charge of organizing the course, said it will help seminary students to become Quran teachers.
It started on June 20 and will run for two weeks, he went on to say.
Al-Mayali noted that more than 40 seminary students have signed up for the Quranic course.
Some of them are from other Muslim countries, he noted.
Quranic activities have significantly developed in Iraq since the 2003 overthrow of former dictator Saddam Hussein.
There has been a growing trend of Quranic programs such as competitions, recitation sessions and educational programs held in the country in recent years.