We report on the discovery of a planetary system with a close-in transiting hot Jupiter on a near circular orbit and a massive outer planet on a highly eccentric orbit . The inner planet , HAT-P-13b , transits the bright V=10.622 G4 dwarf star GSC 3416-00543 every P = 2.916260 \pm 0.000010 days , with transit epoch T _ { c } = 2454779.92979 \pm 0.00038 ( BJD ) and duration 0.1345 \pm 0.0017 d. The outer planet , HAT-P-13c orbits the star with P _ { 2 } = 428.5 \pm 3.0 days and nominal transit center ( assuming zero impact parameter ) of T _ { 2 c } = 2454870.4 \pm 1.8 ( BJD ) or time of periastron passage T _ { 2 ,peri } = 2454890.05 \pm 0.48 ( BJD ) . Transits of the outer planet have not been observed , and may not be present . The host star has a mass of 1.22 _ { -0.10 } ^ { +0.05 } M _ { \sun } , radius of 1.56 \pm 0.08 R _ { \sun } , effective temperature 5653 \pm 90 K , and is rather metal rich with [ Fe / H ] = +0.41 \pm 0.08 . The inner planetary companion has a mass of 0.853 _ { -0.046 } ^ { +0.029 } M _ { J } , and radius of 1.281 \pm 0.079 R _ { J } yielding a mean density of 0.498 _ { -0.069 } ^ { +0.103 } g cm ^ { -3 } . The outer companion has m _ { 2 } \sin i _ { 2 } = 15.2 \pm 1.0 M _ { J } , and orbits on a highly eccentric orbit of e _ { 2 } = 0.691 \pm 0.018 . While we have not detected significant transit timing variations of HAT-P-13b , due to gravitational and light-travel time effects , future observations will constrain the orbital inclination of HAT-P-13c , along with its mutual inclination to HAT-P-13b . The HAT-P-13 ( b , c ) double-planet system may prove extremely valuable for theoretical studies of the formation and dynamics of planetary systems .