Ethiopia does not follow Gregorian calendar because the country uses it's own calendar - Ethiopian calendar. The calendar is used in Eritrea and Ethiopia, it is used as the liturgical year for Christians in Eritrea. The calendar begins on August 29 or August 30.
The Ethiopian calendar is 7 - 8 years behind the Gregorian calendar. The calendar was derived from Egyptian calendar. The calendar is similar to Julian calendar, it adds a leap year every 4 years with out exception.