Which calendar system makes Chinese New Year fall on a different Gregorian date each year?

The lunisolar calendar makes Chinese New Year fall on a different Gregorian date each year.

The traditional Chinese calendar uses both the Moon's phases and the solar year. Chinese New Year begins on the first day of the first month of that calendar, usually between January 21 and February 20 in the Gregorian calendar. Because lunar months are shorter than solar months, an extra intercalary month is inserted in some years to keep the calendar aligned with the seasons.

The celebration lasts fifteen days and ends with the Lantern Festival. Customs include family reunions, red decorations, gift envelopes, fireworks in some places, and foods associated with luck and prosperity. The festival is also called the Spring Festival in mainland China.

It is not accurate to call the traditional system purely lunar. A purely lunar calendar would drift through the seasons. The solar component is what keeps the festival within its familiar winter-to-early-spring range.