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This paper theoretically studies the elastic scattering properties in a mixture of 6Li and 7Li atoms at cold and ultracold temperatures. Based on the constructed accurate interatomic potential of the triplet state for 6Li7Li mixture by the mass scaling method, it calculates the interspecies s-wave scattering lengths and the p-wave scattering lengths by the variable phase method and the semiclassical method, respectively. The scattering length is in good agreement with the experiment. The partial-wave and total cross sections are also calculated and a rich resonance structure is found.