More info please, and a photo if possible.

1. How long have you had the plant?

2. Is it in a pot or in the ground?

3. Are there brown markings on the leaves as well as the flowers?

Since you haven't mentioned anything about spots on the leaves (which I'm sure you would if you had them) the most likely cause of brown spots on the FLOWERS is that the plant isn't getting enough water.
It doesn't matter whether the hydrangea is in a pot or in the ground, except that if it is in a pot it will be easier to move into shade - if the plant is in full sun it will lose a lot of water through its big leaves.
So, water more (evening or early morning is best) and provide sum shade from strong sunlight.