My sister is age of 11,she has no disease but her left hand's wrist veins pain and turns into dark blue colour.

Veins: Blood in veins being deoxygenated looks purplish normally. Veins should not be painful unless they are inflamed(phlebitis) in which case they would be hardened and tender to the touch. My guess is that her hand discomfort is due to other causes such as sprain,contusion,etc. A physician will need to examine her if symptoms persist or if redness or swelling develop.