Granada does have an airport, but It doesn’t have a lot of transit. The closest International airport is The airport of Malaga. From there, you can either take the bus to Granada (2hrs) or the train. We recommend the bus. You can also arrive at Madrid Barajas / Adolfo Suarez International Airport and take the bus to Granada (5hrs).
Can reach more info about in the link: http://www.seimun.es/how-to-arrive/