The spatial resolution of a hyperspectral image is often coarse because of the limitations of the imaging hardware. Super-resolution reconstruction (SRR) is a promising signal post-processing technique for hyperspectral image resolution enhancement. This paper proposes a maximum a posteriori (MAP) based multi-frame super-resolution algorithm for hyperspectral images. Principal component analysis (PCA) is utilized in both parts of the proposed algorithm: motion estimation and image reconstruction. A simultaneous motion estimation method with the first few principal components, which contain most of the information of a hyperspectral image, is proposed to reduce computational load and improve motion field accuracy. In the image reconstruction part, different image resolution enhancement techniques are applied to different groups of components, to reduce computational load and simultaneously remove noise. The proposed algorithm is tested on both synthetic images and real image sequences. The experimental results and comparative analyses verify the effectiveness of this algorithm.