The fraction of absorbed photosynthetically active radiation (fAPAR) is an important plant physiological index that is used to assess the ability of vegetation to absorb PAR, which is utilized to sequester carbon in the atmosphere. This index is also important for monitoring plant health and productivity, which has been widely used to monitor low stature crops and is a crucial metric for food security assessment. The fAPAR has been commonly correlated with a greenness index derived from spaceborne optical imagery, but the relatively coarse spatial or temporal resolution may prohibit its application on complex land surfaces. In addition, the relationships between fAPAR and remotely sensed greenness data may be influenced by the heterogeneity of canopies. Multispectral and hyperspectral unmanned aerial vehicle (UAV) imaging systems, conversely, can provide several spectral bands at sub-meter resolutions, permitting precise estimation of fAPAR using chemometrics. However, the data pre-processing procedures are cumbersome, which makes large-scale mapping challenging. In this study, we applied a set of well-verified image processing protocols and a chemometric model to a lightweight, frame-based and narrow-band (10 nm) UAV imaging system to estimate the fAPAR over a relatively large cultivated land area with a variety of low stature vegetation of tropical crops along with native and non-native grasses. A principal component regression was applied to 12 bands of spectral reflectance data to minimize the collinearity issue and compress the data variation. Stepwise regression was employed to reduce the data dimensionality, and the first, third and fifth components were selected to estimate the fAPAR. Our results indicate that 77% of the fAPAR variation was explained by the model. All bands that are sensitive to foliar pigment concentrations, canopy structure and/or leaf water content may contribute to the estimation, especially those located close to (720 nm) or within (750 nm and 780 nm) the near-infrared spectral region. This study demonstrates that this narrow-band frame-based UAV system would be useful for vegetation monitoring. With proper pre-flight planning and hardware improvement, the mapping of a narrow-band multispectral UAV system could be comparable to that of a manned aircraft system.