Vegetables are naturally low-carb, but the carbohydrates in grains and legumes are complex and don't give a spike in blood sugar. They also have a lot of fiber, which further helps control blood sugar levels. I would suggest including these foods in your diet because they help you to meet requirements for energy, vitamins, minerals, and they are a good source of plant protein. It is recommended that you include at least 6 servings of grains (about 6 slices of whole grain bread or 3 cups of rice or barley/day) and at least 3 servings of legumes (about 1.5 cups/day).
Nuts and seeds are another option for low-carb eating, which you can incorporate into your diet.