Owing to the changing fashion trends and a volatile market situation, demand in fashion and textile (FT) industry is unpredictable and could vary and change completely in a short time, which makes it more difficult to coordinate a FT supply chain. A change in product preference due to fashion trends is the main reason why the demand of FT industry shows more variations than other industries. In this paper, we use a well known contract, the all-unit quantity discount policy (AQDP), to coordinate a FT supply chain with certain demand, and we further consider it under the demand variations scenario to investigate whether it can still coordinate the supply chain. In detail, before the selling season, an AQDP is provided by the manufacturer to the retailer, and under which the FT supply chain coordination achieved with a certain demand. During the selling season, demand variation is realized after an abrupt changing of fashion trends, therefore, the manufacturer may need to revise the original AQDP to insure the supply chain is still coordinated. Utilizing the mechanism design theory, we prove that: (i) while the traditional AQDP can coordinate the supply chain when no demand variations, it cannot always coordinate the supply chain after the demand variations; (ii) when the AQDP fails, we can use the proposed capacitated linear pricing policy (CLPP) to achieve a new coordination; (iii) a more dominant decision maker, who can set a higher profit goal, is favorable to stabilization of the supply chain system under demand variations. Numerical examples are proposed also to show our results.