The sentence is wrong. "He likes fishing" and "He likes to fish" are both correct and mean the same thing. "He likes to go fishing" is also correct, and adds the idea of a fishing _trip_. "He likes to fishing" does not make sense.

The sentence is wrong. It should be "He likes fishing".

"I found this sentence is my sister's English textbook - so there shoudn't be a mistake. Also I decided to google the sentence. And I found many examples of this sentence like " I don't think he likes to fishing that much". I am confused" That's very interesting. I tried a Google search myself. However Google does not insist on exact matches, and most of the hits I found did NOT actually contain the phrase "to fishing." When I did the search on the three-world phrases "likes to fishing", and put the three words within quotation marks, I only got six hits. My belief is that when people write "likes to fishing" they are just making a "slip of the pen." Perhaps they have "likes to fish" and "likes fishing" in their head at the same time. Perhaps they think meant to say "likes to go fishing" and left out the "go." But I could be wrong! Maybe the language is changing and this is the start of something new. Within the last ten years, for example, the use of "because" has changed. Sentences like "because of X" or "because there are X" are now often being shortened to "because X." "Everybody is interested in Salem, Massachusetts, because witches!" I think it's an error, and not changing usage. It's surprising to find it in an English textbook, but if it is e.g. an English textbook written in Ukrainian for Ukrainians, I am sorry to say that you do find occasional errors in textbooks.

Here are two more ideas to consider: "He likes to be fishing" - which is grammatically the same as "he likes to go fishing". The direct object is the infinitive clause "to be fishing" which acts as a noun. "He is happy fishing" - which means the same as "He is happy when he is fishing". The adjective "happy" is a predicative complement. You can think of "fishing" as an adjective modifying "he". That becomes more clear when you write the sentence like this: "Fishing, he is happy".

I think it should be: He likes to "go" fishing.