Many dogs eat grass and subsequently vomit. Others do not vomit after eating grass. It may be they vomit due to grass not being digestible by a dog's system, or due to the grass causing a gag reflex.
Many dogs do seem to do this on purpose as a way of emptying their stomachs though some claim they like the taste. I've seen my pre-labor females eat grass just prior to labor, which I've always assumed was their way of relieving nausea and to clear out their stomach.
You never want to let a dog eat grass that has been treated with fertilizer, weed killers or pesticides or where mushrooms might be. Since grass is not digestible for a dog, if your dog was to eat a large quantity, it could possibly cause a blockage. To curb this behavior, keep your grass well mowed, as they tend to like the longer grass.
I would say your dog has nausea. There are a few things you can try to calm down the stomach. You can give your dog some pepcid at .25 -.5 mg per pound every 12-14 hours.. Read about dosages and usage information here: http://www.petplace.com/drug-library/famotidine-pepcid/page1.aspx
Zantac can be given to a dog at .25 to 1mg per pound every 8-12 hours. Read about usage here:
Pepto-Bismol can be given to a dog at 1 tsp per 5 pounds every 6 hours for upset stomach, gas, or diarrhea.
You may want to offer only bland food such as boiled chicken (1/3) and rice (2/3) for a few days. If he does good, gradually switch him back to his regular food.
If it is possible that your dog ate something toxic such as chocolate, cocoa mulch, antifreeze, medications they will need to see a vet immediately.
I hope one of the above medication calms down your dog's nausea so he can get some rest and recover.