There is stuff called oat grass, ( i call it cat grass). It is safe for them to eat. I started to grow it so that my cats would stop eating my plants. I just grow it in a small rubber bin and put it by a window.
I also have noticed if i don't have it out for a while and then put it out when they first start eating it they do throw up but after a while they stop.
Hope that helps.
It's possible you're cat isn't getting the vitamins and minerals it needs in it's diet? What type of food are you feeding? Be sure it's a good quality human grade food, with a proper amount of wet food.
Otherwise, cats will eat grass if their suffering from an upset stomach. It's a way for them to induce vomiting.
Also, they seem to like it. :-)