We report the discovery of HAT-P-14b , a fairly massive transiting extrasolar planet orbiting the moderately bright star GSC 3086-00152 ( V = 9.98 ) , with a period of P = 4.627669 \pm 0.000005 d. The transit is close to grazing ( impact parameter 0.891 _ { -0.008 } ^ { +0.007 } ) and has a duration of 0.0912 \pm 0.0017 d , with a reference epoch of mid transit of T _ { c } = 2 , 454 , 875.28938 \pm 0.00047 ( BJD ) . The orbit is slightly eccentric ( e = 0.107 \pm 0.013 ) , and the orientation is such that occultations are unlikely to occur . The host star is a slightly evolved mid-F dwarf with a mass of 1.386 \pm 0.045 M _ { \sun } , a radius of 1.468 \pm 0.054 R _ { \sun } , effective temperature 6600 \pm 90 K , and a slightly metal-rich composition corresponding to [ Fe / H ] = +0.11 \pm 0.08 . The planet has a mass of 2.232 \pm 0.059 M _ { J } and a radius of 1.150 \pm 0.052 R _ { J } , implying a mean density of 1.82 \pm 0.24 g cm ^ { -3 } . Its radius is well reproduced by theoretical models for the 1.3 Gyr age of the system if the planet has a heavy-element fraction of about 50 M _ { \earth } ( 7 % of its total mass ) . The brightness , near-grazing orientation , and other properties of HAT-P-14 make it a favorable transiting system to look for changes in the orbital elements or transit timing variations induced by a possible second planet , and also to place meaningful constraints on the presence of sub-Earth mass or Earth mass exomoons , by monitoring it for transit duration variations .