on a diet和on diet都可以说，意思相同。经常跟go或be连用，例如：

on a diet:

You're skinny enough without going on a diet! 你不必节食就已经够瘦的了！

The doctor says I've got to go on a diet. 医生说我得节食。

He's thinned down a lot since he went on a diet.他自从节制饮食以来已经瘦了不少。

I'm supposed to go on a diet.我应该节食。

I think you should go on a diet.我看你应该节食。

The fat boy went on a diet to get rid of his excess weight. 这个胖男孩节制饮食以减轻过量的体重。

He is on a diet to reduce some weight. 他正在节食以减轻体重。

on diet:

It is always not easy to get on diet. 节食减肥却不是那么容易。

They lived on low diet.他们吃粗劣的食物。

I don't want to eat chocolate and junk food; I am on diet.我不吃巧克力和垃圾食品,我在减肥

More and more people, especially females, are to go on diet.越来越多的人, 特别是女生, 开始节制饮食。

You don't need to go on diet. But you can't overeat and should eat limitedly.你不必节食，但要饮食有度，不能吃得过饱。