Bring a large pot of salted water to a boil. Add potatoes and cook until almost tender, about 15 minutes. Add beans and cook until just tender, about 3 minutes. Drain well.
In a large skillet, heat oil over medium heat. Add garlic; cook and stir for 30 seconds. Add the potatoes, beans, and salt and pepper to taste. Cook about 2 minutes more or until heated through, tossing to coat. Add basil and toss once more before serving.