Is this written language, or spoken?

If it's written it's almost okay. I'd just shift the comma:

As a matter of fact, I tried to call you on the telephone this morning, but unfortunately without success..... I couldn't reach you.

As a matter of fact, I tried to call you on the telephone this morning, but unfortunately without success..... I couldn't reach you.

Thank you very much Mini Cooper. Yes, it is in the written (correspondence).

Is it correct, or you think that this sentence can be improved?

It's fine.

I think your version is fine, however:
How about this one:

As a matter of fact, I tried to call you / get hold of you this morning, but unfortunately in vain.

What is nicer (better) in the good correspondence?

As a matter of fact, I tried to call you this morning, but unfortunately in vain.

or

As a matter of fact, I get hold of you this morning, but unfortunately in vain.

Thank you for your comment.

I'd stick with

I tried to call you, because you cannot say that second sentence like that. You "try" to get (a) hold of someone.

Also, unless you are writing a very formal mail or letter, i wouldn't use in vain.

Why don't you use

"As a matter of fact, I tried to call you this morning, but unfortunately I couldn't reach you."