My dream is a traveling the world

Perhaps you meant:
My dream is to travel the world with my family on a big cruise ship.

You would need to clarify what you really meant by "by a big cruise".

Is this write sentence right?

My dream is a traveling the world with my own family on by a big cruise ship.

ozzourtiPerhaps you meant:My dream is to travel the world with my family on a big cruise ship.You would need to clarify what you really meant by "by a big cruise".

Thank you for reply!

That's what I meant.
I want to express that ride a cruise.

Thank you @AlpheccaStars!

Now, I get the wrong parts!

You can say:

I want to cruise with my family around the world on a luxury liner.

"Cruise" is a good verb.

@AlpheccaStars

I didn't know "Cruise" is a verb!
Thank you to teach me good expression

Eom JeongHoI didn't know "Cruise" is a verb!

It can also be a noun. My parents are looking forward to their cruise round the Adriatic.

Thank you for another expression @fivejedjon.

Can I ask something? The "round" is a verb is this sentence? and is there some conjunction omitted?

I really appreciate again.

Round is a preposition in that sentence.

"Round" can have various parts of speech:

The world is round. (adjective)
He rounds off his prices to the nearest dollar. (verb)
We will sail round the world. (preposition)
He is a great golfer. In the tournament, he won the first round, but his opponent won the second. (noun)
The restaurant is open all year round, although the park is closed in the winter. (adverb)