One-year-old babies can eat many kinds of vegetables, as long as they are not cold, they can basically eat them. You can give your baby some potatoes, cauliflower, broccoli, tomatoes, spinach, carrots, celery, zucchini and so on. But it's better to make these vegetables into porridge or cook them for the baby, which is easier to digest. Usually give your baby more fruits and eggs to ensure a balanced diet.