Is it safe to add items to a linked list while iterating

Is it safe to add items to a linked list while iterating?

    final LinkedList<Foo> worklist = new LinkedList<>();

    Iterator<Foo> iterator = worklist.iterator();

    while (iterator.hasNext()) {

        Foo foo = iterator.next();

        doSomethingWith(foo);

        if (expression) {
            worklist.add(new Foo());
        }
    }

If not, how can this behaviour be implemented in a safe and efficient way?

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Note that this is not about a list, but specifically about a linked list (it has to be a linked list in my case). And if it isn't safe to do, I'm asking about alternatives.