We never say "I learn English". We always say "I'm learning English". That is because you are expected to stop learning some time. You can say: I study English. I study English at school. I study English in my free time.

I am learning English......at present I am doing this. I learn English.................I do this everyday,everyweek,.....

The to be+verb-ing construction is called a progressive tense. I am learning English means that you are continually doing it over time. If you say I learn English, than you are saying that that is something that you do. Frankly speaking (To be honest), it describes who you are, since it tells others what you do. You can also say I do learn English. This means that you are emphasizing/stressing the fact that you can speak English and you practice it.

Either one is grammatically correct. It all depends on what context you put the sentence in.