Translation:I have known him for a long time.
It is colloquial to leave out the "for" when using the phrase "a long time."
If your point is true, 'I know him for a long time' should be accepted as well as nothung indicates that I don't know him nomore.
There is no completed action here. I am wondering if it indicates continuous action over the time duration. Does anyone know?
Sentence final 了 does not indicate completed action. That is verb-了. Rather, sentence 了 indicates that the comment is currently relevant. In this case, the speaker is saying that, at the moment of utterance, she has known him a long time. To clarify the function of sentence 了, compare the following two sentences: (1) 我学汉语学了三年。and (2) 我学汉语学了三年了。Sentence (1) indicates that the speaker studied three years of Standard Chinese in the past but is not longer learning the language. Sentence (2) states the same period of study but indicates that the speaker is still currently learning the language. This change in meaning comes from sentence-final 了.