Band selection can greatly increase the efficiency of classification and unmixing of hyperspectral image. Two modified linear-prediction (LP) band selection methods based on similarity are proposed, which measure the information amount of bands through Skewness or Kurtosis and measure the similarity of bands through mutual information (MI) or K-L (Kullback-Leibler) divergence. The least similar two bands with large information amount are selected as the initial two bands, and the rest bands are selected by modified linear prediction. However, the existence of noise bands will affect the result of band selection, making the accuracy of classification or unmixing lower than expected. In order to weaken the adverse effect of noise bands, further efforts are made to estimate the noise of every band through wavelet entropy and remove the bands with considerable noise before band selection. The experiments of classification and unmixing after band selection for real hyperspectral images indicate that linear prediction based band selection can greatly increase the accuracy and efficiency of classification and unmixing , and it is an effective dimensionality reduction method for hyperspectral image.