The grapefruit diet is a commonly known slimming product that has been on the market for a considerable number of years.
This slimming product works on the premise that it has you eating a very low number of calories and then the creators claim that there are special properties in grapefruit that increase the diet's fat burning potential.
The number one ingredient that any slimming product must have is being lower in calories and it is for this reason that this program does work. Be warned however that the level of calories it has you eating is very low and likely not something that would promote overall good health.
The problem with bringing your calories this low is that it will cause a slowing of the metabolic rate and an increase in muscle mass loss therefore increasing the chances that you'll gain back the weight you lost and more after you terminate the diet.
Grapefruit in itself however is a very good fruit to consume on any diet that allows them. It is lower in calories coming in around 70-100 for the whole thing and is a very rich source of vitamin C and fibre. It is also lower on the glycemic index thus it will help to prevent swings in blood sugar levels and feelings of hunger.
While you definitely could go on this program and take advantage of the benefits it has to offer, consider increasing the serving sizes of the meals slightly so that you aren't quite eating as few calories as they suggest. Yes your weight loss may slow slightly but in the long run the chances that you will keep the weight off will be much better.