Here are two very effective exercises that will improve your finger independence.
Basic Exercise (see PDF for tab)
Aim to play as smoothly as possible, keeping each finger in place until the last possible moment. Only lift a finger in order to play the next note on the same string.
Advanced Variation (see PDF for tab)
In this version of the same exercise, the gap between the held notes becomes progressively larger. This makes it very challenging exercise that involves stretches between all combinations of fingers. Make sure you're well warmed up before attempting this one in order to avoid injuries.
Don't worry if you can't go as far as the sixth string; just go as far as is currently comfortable for you. Always focus on maintaining a good legato and holding each finger down for the maximum length of time.