There are many fruits, such as avocados, grapefruits, lemons and limes, that are not naturally sweet. These fruits contain a lower amount of fructose than sweeter fruits.
Avocados, while not normally thought of as a fruit, contain less than 1 gram of sugar per cup of sliced avocado, notes SF Gate. Avocados can help lower blood pressure and stabilize cholesterol levels. Lemons and limes are not sweet to the palate while containing 2 grams or less of sugar. Sour apples, sour grapes and sour cherries are also fruits that are not sweet to the taste. Sour cherries, gooseberries, kumquats and sour apples are not naturally sweet and fall into the category called acid fruits, states The Science of Eating. Acid fruits, while not sweet tasting, are excellent antioxidants as well as being rich in fiber. The amount of fructose in fruit indicates how sweet the fruit tastes.
To minimize the sugar in fruit, it is best to eat the fruit in its raw form, states SF Gate. Dried fruits and fruit juices contain higher levels of sugar. Eating too much sweet fruit with high levels of fructose can lead to diabetes, insulin resistance, high blood pressure, high cholesterol and obesity, explains The Science of Eating.