What kind of tile and what are you cleaning it with?

Do you have a water filter? Perhaps your water is changing the color of your grout? I would try just using a magic eraser with vinegar and water unless you have natural stone anywhere in the shower

I think it is just the color of the grout. From the picture it does not look dirty

I agree with Virginia! It does not look dirty from this pic. Try and go to a professional cleaning supply store. Ask them for suggestions on cleaners you can use to get the results you want.