A faster shutter speed reduces the amount of light entering into your camera, hence your photos are darker.
To answer your question better, you have to be more specific. What's the moving object? How fast is it moving? What kind of condition are you shooting in? Indoor? Outdoor? In any case, I suggest you start by familiarising yourself with some fundamentals on exposure by reading up. Common resources can be obtained from the internet, library or bookshops like Page One, Kino, Riceball, etc.