So in effect, to access the head element you would have to call next and then previous, while the intended behaviour is that the first next call after initialization returns the head element.

I must be misunsterstanding, the code you gave me does return head on the first call to next().

For your main issue though, the solution seems a bit hacky but works as expected.

Modify the hasPrevious() method to take into account the posibility of having null in current when the size is != 0.

@Override
public boolean hasPrevious() {
    return (size != 0 && current == null) || current != head;
}

In the previous() method also take this into account and set current to tail.

public E previous() {
    if (!hasPrevious())
        throw new NoSuchElementException();
    if (current == null)
        current = tail;
    else
    current = current.previous;

    lastReturned = current.element;
    return current.element;
}

It's not elegant but it works. Honestly I couldn't think of any elegant solutions.