Now let’s look at the first one. When we say I worry about you we use the verb to worry in the active form. So the subject is I, the object’s you, so it's a simple subject – verb – object structure (and there’s a preposition between the verb and the object, that’s about).
Now the second one - I am worried about you - starts with a subject, but then it has the verb to be followed by the past participle of the verb worry. Now, you can see that worried operates as an adjective in this sentence; also, the phrase I am worried can be understood as a passive structure, where the passive subject (I) is before the verb and the agent (you) is after the verb (or we don’t mention it at all).
So, which form should you choose for which situation? Well I think that the first one - I worry about you - is a general statement which means that the speaker is generally worried, most of the time, about this person. But the second statement – I am worried – seems to have an element of ‘now’ about it – the speaker seems to be talking about a specific feeling (that’s worry) that he or she has at the time of speaking – and he or she’s mentioned the cause or the reason for the feeling - about you – and that reinforces the idea that the worry is specific to this situation.
So, to show you what I mean, let’s extend the sentences with a bit of context. If I say,
I worry about you – I’m your mother
mothers always worry about their children, it’s not a specific situation, it’s a general situation, I worry about you because I’m your mum.
But if I say,
I’m worried about you, you’re looking very thin
that’s a specific situation. Maybe you’re usually not underweight at all but in this situation I think you look thin and I am worried about you.
So, let’s sum up Mohammad. Both of your sentences are correct, and they mean pretty much the same thing. But if you want to talk about a general, long-lasting worry, say I worry about you, and if you want to talk about a specific worry related to a specific event that’s happening now (or happened recently), you can say I'm worried about you.OK then Mohammad, thanks very much for your question and I do hope you're not too worried about your English!