It's generally a good practice to avoid composting weeds, mainly to avoid spreading them into your garden beds. But that looks like grass to me. If it is grass I would rake it all up into a pile and make sure it was dead before I added it to my compost.
If it's not grass, but rather some type of weed, I wouldn't put it in my compost. You won't be missing much, that much green matter won't turn into very much compost.
