Can heart palpitations be normal?

Yes and no: Particularly as people get older, the heart can beat prematurely or rapidly causing palpitations. That is so common and usually benign so that you might say it is normal. It partly depends on what you mean by normal. Is it normal to have grey hair or wrinkles?

Yes and: Frequently benign but sometimes not...Talk to your physician.

Consult a doctor: It is not normal,but you have not given more details? Avoid caffeine