We report the detection of eighteen Jovian planets discovered as part of our Doppler survey of subgiant stars at Keck Observatory, with follow-up Doppler and photometric observations made at McDonald and Fairborn Observatories, respectively. The host stars have masses 0.927 < Mstar /Msun < 1.95, radii 2.5 < Rstar/Rsun < 8.7, and metallicities -0.46 < [Fe/H] < +0.30. The planets have minimum masses 0.9 MJup < MP sin i <3 MJup and semima jor axes a > 0.76 AU. These detections represent a 50% increase in the number of planets known to orbit stars more massive than 1.5 Msun and provide valuable additional information about the properties of planets around stars more massive thantheSun.