Amo il cibo Italiano is the most exact translation of 'I love Italian food' in Italian, but is not necessarily the most common expression used to convey your love and appreciation of everything from cannelloni to polpette al sugo.
Italians tend not to use the verb amare or 'to love' as freely as we perhaps do in English: Many expressions which we commonly use to profess our love of things like coffee or football are often only 'liked' by Italians - as in mi piace il café or mi piace il calcio. Having said that, to show that you have a particularly strong passion for coffee or football, amo il café or amo il calcio would be perfectly reasonable statements.
Another hitch with the phrase amo il cibo Italiano is that Italians probably wouldn't refer to their national dishes as il cibo Italiano very often. They'd be more likely to use something like la cucina Italiana- literally translating to 'Italian kitchen' and actually meaning something along the lines of 'Italian cuisine'.
Another reason you might not hear Italians commonly referring to 'Italian food' is because most natives will know that the type of food you'd be likely to eat in one region will be markedly different from the type you'd enjoy in another. Italy, as a geo-political entity, has only been a united country as we know it since the late 19th century, and before then independent city-states had their own government, practices and most importantly cuisine - a divide that often remains strong to this day.