Your body absorbs more iron from meat than it does from other sources, according to the Mayo Clinic. So if you stay away from meat, you have to find another way to increase your intake of iron-rich, plant-based foods. Many people opt out for supplements. If meat is out of the question for you, pick foods that are high in Vitamin C to enhance iron absorption. Such foods include broccoli, melons, kiwi, leafy greens, peppers, tomatoes, oranges.