Leaf chlorophyll content (LCC) is an important physiological index to evaluate the photosynthetic capacity and growth health of crops. In this investigation, the focus was placed on the chlorophyll content per unit of leaf area (LCCA) and the chlorophyll content per unit of fresh weight (LCCW) during the tuber formation phase of potatoes in Northern Shaanxi. Ground-based hyperspectral data were acquired for this purpose to formulate the vegetation index. The correlation coefficient method was used to obtain the “trilateral” parameters with the best correlation between potato LCCA and LCCW, empirical vegetation index, any two-band vegetation index constructed after 0–2 fractional differential transformation (step size 0.5), and the parameters with the highest correlation among the three spectral parameters, which were divided into four combinations as model inputs. The prediction models of potato LCCA and LCCW were constructed using the support vector machine (SVM), random forest (RF) and back propagation neural network (BPNN) algorithms. The results showed that, compared with the “trilateral” parameter and the empirical vegetation index, the spectral index constructed by the hyperspectral reflectance after differential transformation had a stronger correlation with potato LCCA and LCCW. Compared with no treatment, the correlation between spectral index and potato LCC and the prediction accuracy of the model showed a trend of decreasing after initial growth with the increase in differential order. The highest correlation index after 0–2 order differential treatment is DI, and the maximum correlation coefficients are 0.787, 0.798, 0.792, 0.788 and 0.756, respectively. The maximum value of the spectral index correlation coefficient after each order differential treatment corresponds to the red edge or near-infrared band. A comprehensive comparison shows that in the LCCA and LCCW estimation models, the RF model has the highest accuracy when combination 3 is used as the input variable. Therefore, it is more recommended to use the LCCA to estimate the chlorophyll content of crop leaves in the agricultural practices of the potato industry. The results of this study can enhance the scientific understanding and accurate simulation of potato canopy spectral information, provide a theoretical basis for the remote sensing inversion of crop growth, and promote the development of modern precision agriculture.