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Isogeometric analysis (IGA) is a relatively new method and receiving much attention recently, the efficient quadrature in which is an important branch far from mature. We introduce the Clenshaw-Curtis quadrature into IGA and give the corresponding algorithms. The estimated computation cost for both rules and of the whole isogeometric approximation are proposed, and through which we compare it with the optimal standard Gauss rule. It is found that the Clenshaw-Curtis rule have better efficiency than the Gauss for spline degree of 2. Better accuracy of CC than Gauss for low spline degrees are also found through the applications of both rules in the boundary value problems.