My green card is about to be expired on July of this year, do I have a problem if it gets expired ?

You have not specified whether you have a ten or two year green card. My answer assumes you have a ten-year green card. You will still be a resident even if the card expires but you will not have valid proof of residency. You should file Form I-90 to renew your green card or consider filing for naturalization. You can read more about naturalization at http://myattorneyusa.com/citizenship-and-naturalization.