The 12-force storm, named Fung Wong, made landfall in southern areas of the island, causing power blackouts in almost 16,000 homes in Hualien County on the east coast.
Schools and offices across Taiwan have been closed, and all domestic flights and 56 international flights have been cancelled.
Fung Wong, Chinese for phoenix, which turned into a strong typhoon at 8:00 p.m. local time on Sunday, is expected to hit land again in southeast China's province of Fujian on Monday night or Tuesday morning.
Authorities in Fujian evacuated 274,300 people and recalled about 52,300 fishing boats on Sunday. Rescuers are helping people on fishing vessels get to the shore.
"The continuous heavy rain is likely to trigger flooding or other secondary disasters," said Yang Zhiying, head of the flood control headquarters in Fujian.
Fung Wong is the eighth and the strongest tropical storm to hit China's coast this year, and comes a week after another tropical storm, Kalmaegi, killed 19 people in Taiwan.
