The large number of spectral bands acquired by hyperspectral imaging sensors allows us to better distinguish many subtle objects and materials. Unlike other classical hyperspectral image classification methods in the multivariate analysis framework, in this paper, a novel method using functional data analysis (FDA) for accurate classification of hyperspectral images has been proposed. The central idea of FDA is to treat multivariate data as continuous functions. From this perspective, the spectral curve of each pixel in the hyperspectral images is naturally viewed as a function. This can be beneficial for making full use of the abundant spectral information. The relevance between adjacent pixel elements in the hyperspectral images can also be utilized reasonably. Functional principal component analysis is applied to solve the classification problem of these functions. Experimental results on three hyperspectral images show that the proposed method can achieve higher classification accuracies in comparison to some state-of-the-art hyperspectral image classification methods.