The spectral uncertainty of terrestrial objects causes a certain degree of spectral differences among feature spectra, which affects the accuracy of object recognition and also impacts the object recognition of spectral angle mapper algorithm (SAM). The spectral angle mapper algorithm is based on the overall similarity of the spectral curves, which was widely used in the classification of hyperspectral remotely sensed information. The spectral angle mapper algorithm does not take the spectral uncertainty of terrestrial objects into account while calculating the spectral angle between the spectral curves, and therefore does not tend to correctly identify the target objects. The applicability of the spectral angle mapper algorithm is studied for the spectral uncertainty of terrestrial objects and a modified SAM is proposed in this paper．In order to overcome the influence of the spectral uncertainty, the basic idea is to set a spectral difference value for the test spectra and the reference spectra and to calculate the spectral difference value based on derivation method according to the principle of minimum angle between the test spectra and the reference spectra. By considering the impact of the spectral uncertainty of terrestrial objects, this paper uses five kaolinite mineral spectra of USGS to calculate the spectral angle between the five kalinite mineral spectra by using local band combination and all bands to verify the improved algorithm. The calculation results and the applicability of the spectral angle mapper algorithm were analyzed. The results obtained from the experiments based on USGS mineral spectral data indicate that the modified SAM is not only helpful in characterizing and overcoming the impact of the spectral uncertainty but it can also improve the accuracy of object recognition to certain extent especially for selecting local band combination and has better applicability for the spectral uncertainty of terrestrial objects.