Is it correct if I don't write 'with' in this sentence?;
I fed up (with) reading this book last year.
I forgot to write 'with' in the above sentence.
But I want to know if the sentence is still grammatically correct without 'with'.
No, it is not correct.
Firstly the phase "fed up with something" is not a past tense verb, it is a participle phrase, so you need
I am fed up with...."
And secondly, while you can say "I'm fed up" (to mean in general) you do need a prepositional phrase "with..." to complete the expression. So it must be "I'm fed up with reading a book."
Talking about "last year" is odd because "I'm fed up" is about now. If you want to talk about becoming fed up you should say
I became fed up with ...
or, more colloquially
I got fed up with ...
(there is a second meaning of "fed up", which is more literal. "I fed up the pig to make it fat", but that is not the use in your example)
First, as I mentioned in a comment either was or got need to come between I and fed up.
If you choose got, you can use the expression without with.
I got fed up reading this book last year.
is perfectly correct. This sentence can be used to mean
I got bored (while) reading the book.
And it makes more sense to me to get fed up with a book than with reading a book, unless someone or something forces you to read it every day:
fed up with: bored, annoyed, or disappointed, especially by something that you have experienced for too long:
- I'm fed up with my job.
- He got fed up with all the travelling he had to do. (Cambridge)
If you choose the verb to be, it should be used in the past, and it could stand if accompanied by with:
I was fed up with reading this book last year. (This sentence does sound somewhat odd to me though.)
or without with:
I was fed up [as I was] reading this book last year. (a comma after fed up could also make sense).
Fed up is an adjective, and as such, it can be preceded by the past tense of the verb to be:
He was fed up with doing all the work. (OxfordL)
Here is an example found in fiction:
She was fed up reading about the lives of people who had more money than sense. (7 Days in May by Peter Barns)