My favorite (unexpectedly involved) project when playing with languages is to write a simple calculator. If you do this on the command line, you'll have to practice parsing strings (or possibly char arrays). If you do it with a GUI, you'll have to practice events (like button presses). And if you're ambitious, you'll implements a GUI that allows you to type as well. If you're feeling really ambitious, make it respect order of operations.
Even if all you do is a four-function calculator, the project is surprisingly involved for a new programmer to accomplish, but you'll learn quite a bit doing it.
so doing this is very useful for learning a languagem then?
I think so. If you've never done anything with programming before, this has potential to be an awfully hard project. Admittedly, this might be a bit beyond your skill level, but I feel you'll progress faster if you have a legitimate challenge, as opposed to a whole bunch of tutorials.
This calculator I'm suggesting...obviously there's more than one way to pulling it off. But every way I can think of pretty well forces you to utilize the fundamentals of the language and programming in general. And if you find it's a bit difficult, shelve it for a week. Figure out what it is has got you stuck, and write a mini-program to teach yourself that function.
You don't have to write a calculator. I'm just suggesting it because it's a challenging project. But as I said, it might be a bit beyond your skill level. Just pick a project more in line with what you understand if that's the case. I'm big on learning by doing, so I believe a great way to learn a language is to pick a challenge and attack it. Ideally, your challenge should be both challenging and utilize the specific skills you want to practice. In your case, this is the basic fundamentals of programming.
I know you said you wanted to do a game, but realistically, I feel like that's just beyond your skill level if you're as new to programming as you said you were. You'll get there...but that'll be project number five or ten, not number one. Work your way up with practical programs and you'll get to the fun ones in due time.
EDIT: I should note that I've never done this particular project in C++. I do have a pretty good idea how I'd do it, but I haven't actually done it. I've focused on other projects when it comes to C++, but I see no reason this should stop you.
Also, C++ is a bit of a challenge for a new programmer. You'll learn a lot doing it, but it'll be hard. You could consider learning programming with Java or Python and then come back to C++ when you understand programming in general a bit better. I am getting the right impression from you posts that you have zero programming experience, right?