Abstract: In combination with the Euler method and predictor corrector technology, an improved iterative method, the Euler predictor corrector algorithm, is proposed, for solving the least squares problems of overdetermined equations. First, the linear least squares problem is transformed into a class of ordinary differential equations, whose solution is then determined by means of the Euler method; then taking its iterative result as the forecast value, the corresponding step parameter is adopted to construct the new iterative formula so as to correct the forecast value, thus to improve the precision of the algorithm, and at last numerical experiments are conducted to prove the feasibility and validity of the said algorithm.