Without looking at the tree itself, I'd say it's either Bacterial Spot disease or Peach Leaf Curl Disease.
It would help, if you could post pictures of the tree and leaves, and tell us the variety and your location.

To me that does not look like peach....where's the fuzz? Maybe a nectarine? Could it be thrips? it looks similar to my problem with my nectarines.

Almost positive it is Thrip damage. See screen capture from UC Davis site showing Thrip damage on Peach and Nectarine.

We purchased it from the nursery and it said it was peach, but maybe not. Here is a photo of the tree itself. If it is thrips what is the solution?

Spinosad. I never tried this, but have read
A little on it. Sounds pretty safe.

Off the topic at hand but maybe helpful in the future. Local nurseries mostly are buying bare root trees from places like stark bros and potting them, letting them grow a bit then sell to you. This process increases the cost and the chances of getting a mislabeled tree. But you gain nothing from it.

So next time cut out the middleman and buy bare root from stark, ACN, Raintree, or others mentioned on this forum

Agree w/ cckw, a good reason to buy from a mail order nursery is the higher probability to receive the actual variety you purchased.

As Puggylover points out, your "peach" is actually some variety of nectarine. Peachlets have "fuzz" right out of the shuck.

This post was edited by olpea on Fri, Apr 25, 14 at 10:56

First, yes, you have a Nectarine tree, not a Peach. As noted above, Peach fruit starts with fuzz and usually has a very pointed end when young.

Your best best is to spray a product like Spinosad when the fruit is just forming in the blossoms - you can see the small fruit inside the flowers. This is when the Thrip feeds and causes the scarring. Spraying once or twice is usually sufficient to take care of most of the damage.

Make sure you spray in the very late afternoon after all bee actively has ceased for the day as Spinosad is toxic to bees for about 3-4 hours after spraying.