We drive a closed-form expression for the price of a European quanto call option in the double square root stochastic volatility model. A quanto is a type of financial derivative whose pay-out currency differs from the natural denomination of its underlying financial variable, which allows that investors are to obtain exposure to foreign assets without the corresponding foreign exchange risk. A quanto option has both the strike price and the underlying asset price denominated in foreign currency. At exercise, the value of the option is calculated as the option's intrinsic value in the foreign currency, which is then converted to the domestic currency at the fixed exchange rate. Pricing options based on the classical Black-Scholes model, on which most of the research on quanto options has focused, has a problem of assuming a constant volatility which leads to smiles and skews in the implied volatility of the underlying asset. For that reason, in valuing quanto option, it is nat- ural to consider a stochastic volatility model. Stochastic volatility models, such as Hull-White model (4), Stein-Stein model (8) and Heston model (3), are frequently used in pricing various kinds of European options. Despite its im- portance, very few researches have been done on pricing quanto option using a stochastic volatility model primarily due to the sophisticated stochastic process for underlying assets and volatilities as well as the difficulty of finding analytic form of the option price. To mention some of the work on pricing quanto options with stochastic volatilities, F. Antonelli et al. (1) used a method of expanding and approximat- ing with respect to correlation parameters to find analytic formula of exchange options with stochastic volatilities. Using the technique developed in (1), J. Park et al. (6) got an analytic approximation value for a quanto option price in the Hull-White stochastic volatility model. A. Giese (2) provided a closed-form