Vehicle-to-Infrastructure (V2I) communication has provided a solution for the improvement of the traffic efficiency of smart city intersections. For example, turning maneuvers prediction at signalized intersections in a connected environment helps traffic command centers time traffic lights and dynamically predict traffic flow. However, the modeling methods used in existing research on this topic have some limitations, such as poor scalability and interpretability of machine learning. Thus, this study proposes a dictionary learning-based approach to predict turning maneuvers before the intersection. The proposed dictionary model estimates the LogDet divergence-based sparse inverse covariance matrix (LDbSICM) of driving behavior samples. The graphical lasso method is used to estimate the sparse inverse covariance matrix of the driving samples to construct a dictionary library of the maneuver behavior. The LogDet divergence is used to calculate the difference between each inverse covariance matrix. A driving simulator is utilized to collect experimental data consisting of turning left (TL), turning right (TR), and going straight (GS) behaviors to establish and evaluate the proposed model. The experimental results demonstrate that the proposed dictionary learning-based turning maneuver prediction model achieves 100% prediction accuracy for TL and GS and 97.2% for TR. The proposed model has substantial advantages over existing methods. The model can predict TL, TR, and GS in a connected environment 270, 280, and 290 m, respectively, before the intersection.