The 80-tonne Jih-chun Tsai 68 with captain Wu Lai-yu and 10 Indonesian crew was hijacked in March 2010 while sailing in waters off Somalia.
Wu was killed earlier this month in crossfire between the pirates and the USS Stephen W. Groves when the pirates used the fishing boat to launch attacks, Taiwan`s foreign ministry said in a statement late Saturday.
The fishing vessel was sunk and three pirates killed, it said.
"We`ve expressed concerns to the United States," foreign ministry spokesman Steve Shia told AFP Sunday.
"We`ve also asked the American Institute in Taiwan to come up with an investigation report about the incident," he said, referring to the de facto US embassy in Taipei.
Wu`s family had been in negotiations with the pirates for his release, but no agreement had been reached over the amount of ransom. The 10 Indonesian crew were released in March but it was not immediately clear if the shipowner had paid any ransom for them.
Piracy has surged in recent years off Somalia, a lawless, war-torn country that sits alongside one of the world`s most important shipping routes.
Despite the scale of piracy off Somalia, only a few perpetrators have been brought to justice so far. Many of those caught by an international fleet of warships are freed because there is nowhere to try them. (*)