Tips:
Put fabric tents up over cabbage plants, Brussels sprouts, and broccoli to keep away garden pests. Sprinkle cabbage heads with cinnamon and the cabbage worms will stay away. -source
Try planting red leafed varieties of cabbage and kohlrabi, which are less appealing to cabbage worms due to the lack of camouflage. More than one species of cabbage worm can be on the same plants at the same time, so be vigilant in your inspections.

Preventing Problems:
You can use row cover to prevent egg laying by adults if you frequently have trouble with cabbage worms in spring. Plant lots of flowers and blooming herbs around your cabbage patch to provide a strong supply of nectar for beneficial insects, such as paper wasps, yellow jackets, shield bugs and insect eating birds.

HOW TO GET RID OF CABBAGE WORMS
Manually remove (handpick) the eggs if possible.
Yellow sticky traps will catch the adult butterflies, but may also catch beneficial insects. And, the few pests that remain on the vegetables can be washed out after harvest using water and a small amount of detergent or other surfactant.
It is said that if you dampen cabbage leaves and sprinkle them with cornmeal, the caterpillars will eat the meal, swell, and die.
Check with your local Cooperative Extension for your area’s regulations on chemical control.
Old folk advice from The 1963 Old Farmer’s Almanac states: Years ago, people sprinkled rye flour over cabbage plants in the early morning. The flour dehydrated the cabbage worms. Give it a try!

PREVENT CABBAGE WORMS
Cover your plants with row covers to deter the adult butterflies from laying eggs on the cabbages. Trichogramma wasps (very tiny; they do not sting humans) parasitize the eggs of the imported cabbage worm; these beneficial insects are available by mailorder, although you’ll need to time their release appropriately—the mailorder company would be able to help you.
Read more about beneficial insects.
Companion planting is a useful deterrent for many pests. Cabbage worms are repelled by thyme, so it would be a good idea to plant thyme near your susceptible plants. Cabbage worms are attracted to mustard plants, so planting mustard near more valuable plants can be a good trap for cabbage worms. Once they take over the mustard, you can destroy the plant.
Try planting red leafed varieties of cabbage. The cabbage worms won’t be able to camouflage, so they are less likely to choose these plants

PLANTS AFFECTED
Cabbage
Kale
Cauliflower
Broccoli