The main TAIEX share index closed up 71.96 points at 5,870.37, extending a 2.9 percent rebound in the previous two sessions from the lowest level in 14 months.
"Buying by foreign investors was a signal that they still have hopes of more upside for the market," said Kevin Lin, a fund manager at Shinkong Investment Trust.
Turnover stood at T$74.53 billion ($2.22 billion) on Wednesday, down from T$77.0 billion on Tuesday.
The heavily weighted electronics sub-index rose 1.68 percent and the financial sector edged up 0.64 percent.
Among the major winners, Quanta Computer Inc, the world's largest contract maker of laptop computers, gained 1.68 percent and electronics components maker Hon Hai Precision Industry Co was up 1.66 percent.