The carrier entered the strait that separates the island and mainland China on Wednesday afternoon "sailing from south to north along the west of the median line of the strait," Taipei's defence ministry said.
"As of 8 am today (0000 GMT), it has continued to sail northward through the northern waters," the ministry said in a statement.
Taiwan's military was closely monitoring the situation and had tasked appropriate forces to respond, it added.
Last month, another formation led by the Shandong entered the Pacific Ocean via the Bashi Channel, a waterway that separates Taiwan from the Philippines, according to Taipei.
In September, the Shandong, one of the two operational aircraft carriers in the Chinese fleet, was detected around 60 nautical miles (110 kilometres) southeast of Taiwan heading into the Western Pacific.
Taiwan has seen a ramp-up in military and political pressure in recent years from Beijing, which considers the self-ruled island its territory and has vowed to seize it one day -- by force if necessary.
The Shandong's latest passage through the Taiwan Strait came after China said its troops were "on constant high alert" after US and Canadian warships transited through the sensitive waterway last week.
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