Pairing-based cryptosystems have been developing very fast in the last few years. The efficiencies of the cryptosystems are determined by the computation of the Tate pairing. In this paper a new efficient algorithm based on double-base chain for computing the Tate pairing is proposed for odd characteristic p > 3. The inherent sparseness of doublebase number system reduces the computational cost for computing the Tate pairing evidently. It is 9% faster than the previous fastest method for MOV degree k=6.