The Leaf Area Index (LAI) is a crucial indicator of crop photosynthetic potential, which is of great significance in farmland monitoring and precision management. This study aimed to predict potato plant LAI for potato plant growth monitoring, integrating spectral, textural, and morphological data through UAV images and machine learning. A new texture index named VITs was established by fusing multi-channel information. Vegetation growth features (Vis and plant height Hdsm) and texture features (TIs and VITs) were obtained from drone digital images. Various feature combinations (VIs, VIs + TIs, VIs + VITs, VIs + VITs + Hdsm) in three growth stages were adopted to monitor potato plant LAI using Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), random forest (RF), and eXtreme gradient boosting (XGBoost), so as to find the best feature combinations and machine learning method. The performance of the newly built VITs was tested. Compared with traditional TIs, the estimation accuracy was obviously improved for all the growth stages and methods, especially in the tuber-growth stage using the RF method with 13.6% of R2 increase. The performance of Hdsm was verified by including it either as one input feature or not. Results showed that Hdsm could raise LAI estimation accuracy in every growth stage, whichever method is used. The most significant improvement appeared in the tuber-formation stage using SVR, with an 11.3% increase of R2. Considering both the feature combinations and the monitoring methods, the combination of VIs + VITs + Hdsm achieved the best results for all the growth stages and simulation methods. The best fitting of LAI in tuber-formation, tuber-growth, and starch-accumulation stages had an R2 of 0.92, 0.83, and 0.93, respectively, using the XGBoost method. This study showed that the combination of different features enhanced the simulation of LAI for multiple growth stages of potato plants by improving the monitoring accuracy. The method presented in this study can provide important references for potato plant growth monitoring.