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As one of the fitting methods,the polynomial approximation is effective to process sophisticated problem.In this paper,we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole.The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximatepolynomial.The SchrSdinger-like equation,the real boundary conditions and the polynomial approximation constructa full Sturm-Liouville type problem.Then this boundary value problem can be solved numerically for two limitingcases:the first one is the Nariai black-hole whose horizons are close to each other,the second one is the black-hole withthe horizons widely separated.Compared with previous results (Brevik and Tian),the field near the event horizon andcosmological horizon can have a better description.