There are many reasons why you may still be getting some tan despite diligent use of sunscreen. One likely cause is the fact that even the best of sunscreens still let some sun rays through. A high SPF number is not about better or deeper protection, but only longer protection.
High SPF numbers give the false impression they can provide enhanced protection when that is not the case. A well-formulated sunscreen with an SPF 70 still only protects your skin from about 98% of the sun’s rays.
That means 2% of the sun’s rays are still getting through, and that can trigger melanin production, the skin’s tanning response.
This is especially true for those with darker skin tones or for those who have a lot of previous sun damage, because for them hypermelanin production is more likely to take place.
from: The Original Beauty Bible by Paula Begoun
What does this mean for you?
Don't rely only on a sunscreen to prevent sun damage & tanning. Look at multiple levels of protection. So along with an sunscreen, also consider using a cap / scarf / sunglasses / umbrella.