Vegetation index is a simple, effective and experiential measurement of terrestrial vegetation activity, and plays a very important role in qualitative and quantitative remote sensing. Aiming at shortages of current vegetation indices, and starting from the analysis of vegetation spectral characteristics, we put forward a new vegetation index, the three-band gradient difference vegetation index (TGDVI), and established algorithms to inverse crown cover fraction and leaf area index (LAI) from it. Theoretical analysis and model simulation show that TGDVI has high saturation point and the ability to remove the influence of background to some degree, and the explicit functional relation with crown cover fraction and LAI can be established. Moreover, study shows that TGDVI also has the ability to partly remove the influence of thin cloud. Experiment in the Shunyi District, Beijing, China shows that reasonable result can be reached using the vegetation index to retrieve LAI. We also theoretically analyzed the reason why the normalized difference vegetation index (NDVI) owns the low saturation point, and show that it is determined by the definition of NDVI and the characteristic of vegetation spectra, and is unavoidable to some degree. Meanwhile, through model simulation, we also indicate that the relationship between simple ratio vegetation index (SR) and LAI closes to a piecewise linear one instead of a linear one, which is mainly caused by the influence of background and different change rates of reflectance in red and infrared bands with LAI increasing.