Have you tried Internet Recovery? This may work if there is something wrong with the Recovery disk on your Mac. Hold down Command plus Option plus R when starting up. You will need a good internet connection and will get a spinning globe at first and it may take a while to load the Utility window.
Can you give more details about your Mac, such as how old it is and what kind of drive, SSD or rotating, etc.? It could be that your hard drive is failing.
It may be best to take it in to an Apple Store to have it checked. Contact - Official Apple Support