With the increasing popularity of Android smartphones, malware targeting the Android platform is showing explosive growth. Currently, mainstream detection methods use static analysis methods to extract features of the software and apply machine learning algorithms for detection. However, static analysis methods can be less effective when faced with Android malware that employs sophisticated obfuscation techniques such as altering code structure. In order to effectively detect Android malware and improve the detection accuracy, this paper proposes a dynamic detection model for Android malware based on the combination of an Improved Zebra Optimization Algorithm (IZOA) and Light Gradient Boosting Machine (LightGBM) model, called IZOA-LightGBM. By introducing elite opposition-based learning and firefly perturbation strategies, IZOA enhances the convergence speed and search capability of the traditional zebra optimization algorithm. Then, the IZOA is employed to optimize the LightGBM model hyperparameters for the dynamic detection of Android malware multi-classification. The results from experiments indicate that the overall accuracy of the proposed IZOA-LightGBM model on the CICMalDroid-2020, CCCS-CIC-AndMal-2020, and CIC-AAGM-2017 datasets is 99.75%, 98.86%, and 97.95%, respectively, which are higher than the other comparative models.