The 64bit HP LaserJet Pro P1108 Printer driver has been added below and you will note that it uses the same driver as the LaserJet Pro P1560 Printer also listed on this website. This is a 64bit driver only for the Windows 10 as well as the Windows 7 and Windows 8 and 8.1 operating systems. Search this website should you not be able to download or install the driver. There are a number of drivers only HP drivers on this website.
Download and open the file below. Then click on the file inside and the driver fro the HP printer should install.
Windows 2003 / XP 64 bit / 2008 / Vista 64 bit / 7 64 bit / 8 64 bit / 8.1 64 bit / 10 64 bit / Mac