We report the detection of a double planetary system around the evolved intermediate-mass star HD 47366 from precise radial-velocity measurements at Okayama Astrophysical Observatory, Xinglong Station, and Australian Astronomical Observatory. The star is a K1 giant with a mass of 1.81+-0.13M_sun, a radius of 7.30+-0.33R_sun, and solar metallicity. The planetary system is composed of two giant planets with minimum mass of 1.75^{+0.20}_{-0.17}Mjup and 1.86^{+0.16}_{-0.15}Mjup, orbital period of 363.3^{+2.5}_{-2.4} d and 684.7^{+5.0}_{-4.9} d, and eccentricity of 0.089^{+0.079}_{-0.060} and 0.278^{+0.067}_{-0.094}, respectively, which are derived by a double Keplerian orbital fit to the radial-velocity data. The system adds to the population of multi-giant-planet systems with relatively small orbital separations, which are preferentially found around evolved intermediate-mass stars. Dynamical stability analysis for the system revealed, however, that the best-fit orbits are unstable in the case of a prograde configuration. The system could be stable if the planets were in 2:1 mean-motion resonance, but this is less likely considering the observed period ratio and eccentricity. A present possible scenario for the system is that both of the planets have nearly circular orbits, namely the eccentricity of the outer planet is less than ~0.15, which is just within 1.4sigma of the best-fit value, or the planets are in a mutually retrograde configuration with a mutual orbital inclination larger than 160 degree.
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