A new adaptive recursive algorithm for eigenvector estimation based on the relations between KLT and sliding DCT was presented. On the basis of the equivalence of weight vector of an adaptive filter and the eigenvector, choosing a reasonable filter expectation response, the eigenvector was estimated. Compared with current eigenvector calculation methods such as SVD, the proposed algorithm can effectively reduce both amount of calculation and complexity, be easily implemented on time, and possesses high estimation accuracy. Applying this algorithm in spectrum estimation with computer simulations, it is known that the proposed recursive eigenvector estimation algorithm attains higher spectrum estimation solution comparing with standard MUSIC spectrum estimation method with less calculation, which proves the effectiveness and advantage of the algorithm.