Abstract: The linear-quadratic expected regression model, which consisted of a straight line and a quadratic curve intersecting at a change point, could not only capture the change point effect in data, but also provide a complete picture of the response variance through tail expectation. Estimating the change point and other parameters of the model was not easy and directly by traditional optimization methods due to the existence of the change point. This article proposed a new estimation method via a linearization technique to estimate the regression coefficients and the change point simultaneously. Statistical inferences of the proposed estimators are easily derived from the existing theory. Numerical simulations show that the estimation has good validity and robustness, and empirical research on the life expectancy at birth and gross domestic product (GDP) per capita data also demonstrates the model and method are feasible and practical.