We have synthesized a new spinel oxide LiRh2O4 with a mixed-valent configuration of Rh3+ and Rh4+. At room temperature, it is a paramagnetic metal, but on cooling, a metal-insulator transition occurs and a valence bond solid state is formed below 170 K. We argue that the formation of valence bond solid is promoted by a band Jahn-Teller transition at 230 K and the resultant confinement of t_{2g} holes within the xy band. The band Jahn-Teller instability is also responsible for the observed enhanced thermoelectric power in the orbital-disordered phase above 230 K.