I have some problems to access the list by iterator accordingly.

1. The list 'mylist_' and struct 'i' have to be redefined in a class file. Should it be done once in a header file? I have tried but have got a Segmentation fault error.

2. When I call the function 'list()', I would like to append a new entry to the list. The list size should grows up while calling list(). But this never happens, mylist_size() is always 1.

3. In the function 'getlist()', the iterator shows strange values of the list even it works fine in the function 'list()'.

Herewith, I attached an example of my code. Any suggestion, I am very welcome to hear

#aaa.h
struct mystruct {
double x
double y
}
class aaa {
public :
void list();
void getlist();
list< struct mystruct > mylist_;
struct mystruct i;
}

#aaa.cc
void aaa::list(){
list< struct mystruct > mylist_;
struct mylist i;

i.x = 10.0;
i.y = 20.0;

mylist_.push_back(i);

list< struct mystruct >::iterator it;
for(it = mylist_.begin() ; it != mylist_.end() ; it++) { 
cout<< it->x << " , "<< it->y << endl; <-- ok!!
}
}

void aaa::getlist(){
list< struct mystruct >::iterator it;
for(it = mylist_.begin() ; it != mylist_.end() ; it++) {
cout<< it->x << " , "<< it->y << endl;  <-- strange values!!
}
}

- the variables i and mylist_ should be made private members of your class aaa (granting public access to class member variables breaks encapsulation)
- unlike in C, in C++ there is no need to qualify mystruct as struct everytime. That means, list<mystruct> is sufficient and the declarations of i can (or should) be abbreviated to mystruct i; because mystruct is a complete type specifier on its own.
- the definition of mylist_ in aaa::list() defines a local variable, so the name of the member aaa.mylist_ is hidden. this is probably NOT what you want. The same applies to mystruct i. The result is that you construct a local struct, stuff it in the local list and do the output. After that at the end of aaa::list() both local variables are destroyed. Therefore, when calling aaa::getlist() that method accesses the aaa member variables that have never been touched.
what actually confuses me is that you seem to get into the for-loop inaaa:getlist(). As I said, you never touched the member mylist_ (you only modified the local variable mylist_ in aaa::list()). When you say mylist_.size() is 1 everytime that means you must have put something into the list in aaa's constructor - and the "strange values" in getlist() are those values from the ctor.

Or you can google other examples with list or other keywords.

list< struct mystruct > mylist_;

You don't have to write the struct here. You just have to use the keyword struct in a definition.

list< mystruct > mylist_;

Would do this.