We present evidence for a new two-planet system around the giant star HD 202696 ( = HIP 105056 , BD +26 4118 ) . The discovery is based on public HIRES radial velocity ( RV ) measurements taken at Keck Observatory between 2007 July and 2014 September . We estimate a stellar mass of 1.91 ^ { +0.09 } _ { -0.14 } M _ { \odot } for HD 202696 , which is located close to the base of the red giant branch . A two-planet self-consistent dynamical modeling MCMC scheme of the RV data followed by a long-term stability test suggests planetary orbital periods of P _ { b } = 517.8 _ { -3.9 } ^ { +8.9 } and P _ { c } = 946.6 _ { -20.9 } ^ { +20.7 } days , eccentricities of e _ { b } = 0.011 _ { -0.011 } ^ { +0.078 } and e _ { c } = 0.028 _ { -0.012 } ^ { +0.065 } , and minimum dynamical masses of m _ { b } = 2.00 _ { -0.10 } ^ { +0.22 } M _ { \mathrm { Jup } } and m _ { c } = 1.86 _ { -0.23 } ^ { +0.18 } M _ { \mathrm { Jup } } , respectively . Our stable MCMC samples are consistent with orbital configurations predominantly in a mean period ratio of 11:6 and its close-by high-order mean-motion commensurabilities with low eccentricities . For the majority of the stable configurations , we find an aligned or anti-aligned apsidal libration ( i.e . \Delta \omega librating around 0 ^ { \circ } or 180 ^ { \circ } ) , suggesting that the HD 202696 system is likely dominated by secular perturbations near the high-order 11:6 mean-motion resonance . The HD 202696 system is yet another Jovian-mass pair around an intermediate-mass star with a period ratio below the 2:1 mean-motion resonance . Therefore , the HD 202696 system is an important discovery , that may shed light on the primordial disk-planet properties needed for giant planets to break the strong 2:1 mean motion resonance and settle in more compact orbits .