Hunter Biden had worked for Burisma, is one of the largest natural gas producers in Ukraine, between 2014 and 2019, Efe news reported.
"The campaign against the Ukrainian oil and gas company was launched by the Main Intelligence Directorate of the General Staff of the Russian Army or GRU," the eight-page report by Area 1 Security, the Silicon Valley-based cyber-security firm, said on Monday.
According to Area 1, the phishing attacks targeting Burisma began last November, a month after the Democrats launched a formal impeachment inquiry against US President President Donald Trump.
The aim of the Russian hackers allegedly was to obtain information intended to harm the Biden family, according to The New York Times citing cyber-security experts.
The hackers allegedly tried to steal information from Burisma using different techniques. For example, they created fake websites that resembled the login pages of Burisma's subsidiaries.
They also sent emails to Burisma's employees that resembled the company's internal communications, according to the report.
Several US media outlets, believe that there was a parallel with the computer attack against the team of Trump's rival Hillary Clinton and the Democratic National Committee during the 2016 presidential campaign.
In that case, US intelligence agencies concluded in a 2017 report that Russian President Vladimir Putin had ordered an influence campaign aimed at the US election through cyberattacks because he had a "clear" preference for Trump.
Both Moscow and Trump have rejected these claims.
The alleged attack on Burisma occurred in the context of the impeachment of Trump, who Democrats accuse of having pressured his Ukrainian counterpart, Volodymyr Zelensky, to open an investigation for corruption against the Biden family in an attempt to hurt him in the face of this year's election.
Trump, who is running for re-election, is awaiting the start of the impeachment trial in the Senate.
( With inputs from IANS )