As Maroon points out in a comment, you have to say which dialect you are asking about. This answer is for Standard Chinese, aka Mandarin.
It also depends on what sort of stuff you include. Counting the distinct lines in the syllable index of the Pinyin Chinese-English Dictionary, I get 420 "lines" but this includes some very marginal stuff such as tei, kei, den, etc. This does not include any of the rhotacized syllables, where a suffix -er merges with the syllables and produces many distinctive syllables.
Most important, however, this figure ignores the four lexical tones of Mandarin, which is definitely not the right; tones are distinctive in Mandarin, so syllables with different tones are different syllables. The distribution of tones and syllables is skewed, however; not every syllable has all four tones. A rough approximation is about 1200 distinct syllables. Again, there will be many marginal cases.
All this does not use any sort of phonemic analysis which could perhaps reduce the number of syllables, depending on what phonological theories or notation you adopt.
So Chinese is not so syllable poor as you might expect. Japanese and Hawaiian, for example, have far fewer distinct syllables than Mandarin.