This paper investigates an efficient estimation method for a cointegrating regression model with structural change. Our proposal is that we first estimate the break point by minimizing the sum of squared residuals and then, by replacing the break fraction with the estimated one, we estimate the regression model by the canonical cointegrating regression (CCR) method proposed by Park (1992). We show that the estimator of the break fraction has the same convergence rate as obtained in Bai, Lumsdaine and Stock (1998) and that the CCR estimator with the estimated break fraction has the same asymptotic property as the estimator with the known break point. Simulation experiments reveal how the finite sample distribution gets close to the limiting distribution as the magnitude of the break and/or the sample size increases.