Asian rainbow option is option on the minimum or the maximum of several average prices. In modern financial market, Asian rainbow option is an effective instrument for asset allocation and risk management. The investor with Asian rainbow option enjoys an entitlement to select a max or min from multiple assets with an exercise price at maturity date. The investor has to defray fee to acquire this right, which raises the option pricing issue. This paper mainly explores the pricing of Asian rainbow option in the uncertain financial environment, in which the underlying assets prices are treated as uncertain processes. Here, the pricing formulas of Asian rainbow option are derived under the condition that stock prices obey uncertain differential equations driven by independent Liu processes. Furthermore, some numerical examples are designed to compute the prices of these options.