The Croatian president met in Doha with Qatar's Prime Minister, Sheikh Abdullah bin Nasser bin Khalif Al-Thani, and on Sunday she was expected to hold talks with the country's Emir, Sheikh Tamim bin Hamad bin Khalif Al Thani.
Qatar's business appeal lies in high living standards enabled by large oil and gas reserves.
Energy products account for 90% of Qatar's exports and more than 75% of the budget revenues of that emirate with a population of some 2.5 million, of whom 310,000 are Qatari citizens.
Qatar earlier expressed an interest in a plan to build and LNG terminal on the Croatian northern Adriatic island of Krk, a strategic project of Croatia and the EU which should be put into operation in 2019 and which is aimed at reducing Europe's dependence on Russian gas.
"Qatar is one of the countries where decisions are made at high levels of authority so more frequent mutual visits increase chances for our economy," Grabar-Kitarovic told reporters.
"I hope that with the Qatari leadership and at direct talks between our business people we will lay foundations for the participation of Croatian business people in the Qatari market and for potential Qatari investments in Croatia," she said.
Attending the talks between Grabar-Kitarovic and the Qatari prime minister were also Croatian Army Main Staff director Robert Hranj, Croatian Chamber of Commerce president Luka Burilovic and the head of the Islamic community in Croatia, Mufti Aziz Hasanovic.
The Croatian delegation said that the good political and economic relations between the two countries could also be attributed to the excellent relations between Croatian Muslims and the leaders of Qatar, which has financed the construction of a mosque in Rijeka, opened in 2013.
Members of the Croatian delegation said they were pleasantly surprised by the warm welcome they received in Doha, which was visited by almost all most senior Croatian officials in the last ten years.
Sheikh Abdullah Al-Thani interrupted his vacation because of the visit of the Croatian delegation, and the Croatian president also had a private audience with the former Emir of Qatar Hamad bin Khalifa Al-Thani, who spent several summer vacations sailing along the Croatian Adriatic coast.
On Sunday, the Croatian president is due to visit the Qatar Foundation for Education, Science and Community Development and meet with the former emir's wife, Sheikha Mozah bint Nasser, who runs that institution.
At the end of the visit, a Croatian-Qatari business forum will be held.