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We report the discovery of a new hot-Jupiter, KOI-196b, transiting a solar-type star with an orbital period of 1.855558 days +/- 0.6 s thanks to public photometric data from the Kepler space mission and new radial velocity observations obtained by the SOPHIE spectrograph mounted on the 1.93-m telescope at the Observatoire de Haute-Provence, France. The planet KOI-196b, with a radius of 0.89 +/- 0.05 R-Jup and a mass of 0.55 +/- 0.09 M-Jup, orbits a G6V star with R-star = 1.02 +/- 0.03 R-circle dot, M-star = 1.12 +/- 0.07 M-circle dot, [Fe/H] = 0.29 +/- 0.16 dex, T-eff = 5620 +/- 140 K, and an age of 650(-300)(+2500) Myr. KOI-196b is one of the rare close-in hot Jupiters with a radius smaller than Jupiter suggesting that it is a non-inflated planet. The high precision of the Kepler photometry permits us to detect the secondary transit with a depth of 64(-12)(+10) ppm as well as the optical phase variation. We find a geometric albedo of A(g) = 0.30 +/- 0.08, which is higher than most of the transiting hot Jupiters with a measured A(g). Assuming no heat recirculation, we find a day-side temperature of T-day = 1730 +/- 400 K. The planet KOI-196b seems to be one of the rare hot Jupiters located in the short-period hot-Jupiter desert.