Abstract: Householder transform is used to triangularize the data matrix which is based on the linear prediction error equation. It is proved that the sum of squared residuals for each AR order can be obtained by the main diagonal elements of upper triangular matrix, so the column by column procedure can be used to develop a recursive algorithm for AR modeling and spectral estimation. In the most cases, the presented algorithm yield the same results as the covariance method or modified covariance method does. But in some special cases where the numericall ill-conditioned problems are so serious that the covariance method and inodified covariance method fail to estimate AR spectrum, the presented algorithm still tends to keep good performance. The typical computational results are given finally.