Lane changing is a frequent traffic accident scenario. To improve the driving safety in lane changing scenarios, the blind spot display of lane changing is increased through human–machine interaction (HMI) interfaces in intelligent vehicles to improve the driver’s rate of risk perception with regard to the driving environment. However, blind spot information will increase the cognitive load of drivers and lead to driving distraction. To quantify the coupling relationship between blind spot display and drivers’ cognitive load, we proposed a method to quantify the cognitive load of the driver’s interaction by improving the AttenD algorithm, collecting feature data by carrying out a variety of real-vehicle road-testing experiments on three kinds of intelligent vehicles, and then establishing a model blind spot design and driver cognitive load correlation model using Bayesian Logistic Ordinal Regression (BLOR) and Categorical Boosting (CatBoost). The results show that the blind spot image display can reduce the driver’s cognitive load more effectively as it is closer to the driver, has a larger area, and occupies a higher proportion of the center control screen, especially when it is located in the middle and upper regions of the center control screen. The improved AttenD algorithm is able to quantify the cognitive load of the driver, which can be widely used in vehicle testing, HMI interface development and evaluation. In addition, the analytical framework constructed in this paper can help us to understand the complex impact of HMI in intelligent vehicles and provide optimization criteria for lane change blind spot design.