The problem of numerical interpolation is encountered in many engineering and scientific applications. Newton's methods are commonly used to solve these problems. Generally, Newton's algorithms are of O(n 2 ) sequential complexity. In this paper, Newton's divided difference interpolation algorithm is reorganized to well-suite vector processing. The proposed algorithm has O(log n) vector complexity. It requires 2 log n + 4 vector instructions to set up the divided differences, and log n + 4 vector instructions to evaluate the interpolating polynomial at a given point.