When you strum upwards, do not try to strum all the strings. Even if you are playing an open position G chord which spans all six strings, you would only really catch 3 or maybe four strings on the way up.

I would also recommend using a stiff pick and try to achieve a nice sound. This will help you to develop a relaxed and controlled strumming action, even if it sounds terrible at first. Too often beginners reach for the really thin pick to compensate for a lack of technique, and continue to bash at the strings.

I hope this helps.

John