After graduation, he worked as a senior veterinarian in the livestock department of the inter-farm complex for growing and fattening cattle "Vyselkovsky".
In 2001, Gromyko was appointed general director of the Department of Regional Food of the Krasnodar Krai.
The same year, he became the advisor to Alexander Tkachov, who was the head of the administration of the Krasnodar Krai.
From 2009 to 2012, Gromyko served as Deputy Head of Administration (Governor) of the Krasnodar Krai Alexander Tkachev.
From January 2014 to July 2015 Gromyko represented Krasnodar Krai in the Federation Council.