Berry will travel Taiwan until February 3 and is scheduled to meet with Government officials and LGBT activists.
It is part of a six-country trip that will also include Vietnam, Thailand, Indonesia, South Korea and Japan.
He will arrive in Taiwan on January 31 and "discuss ways in which likeminded partners can work together to strengthen the global commitment to LGBTI rights," according to the American Institute in Taiwan.
Berry assumed the newly created position in April 2015.
He has just finished an 11-day trip of Africa in which he visited Malawi, Namibia, Botswana and South Africa.