We present a novel speech enhancement method based on locally linear embedding (LLE). The proposed method works as a post-filter to further suppress the residual noises in the enhanced speech signals obtained by a speech enhancement system to attain improved speech quality and intelligibility. We design two types of LLE-based post-filters: the direct LLE-based post-filter (called the DL post-filter) and the LLE-based difference compensation post-filter (called the LDC post-filter). The key technique of the proposed post-filters is to apply the LLE-based feature prediction method, which integrates the LLE algorithm, a classical manifold learning method, with the exemplar-based feature prediction method, to predict either the spectral features of the clean speech from those of the enhanced speech (for DL) or the spectral difference of {clean speech; noisy speech} from that of {enhanced speech; noisy speech} (for LDC). As a result, for DL, the predicted clean speech signals can be directly reconstructed from the predicted clean spectral features. On the other hand, for LDC, the predicted clean spectral features are obtained by compensating the spectral features of the noisy speech with the predicted clean-noisy spectral difference, and then the predicted clean speech signals can be reconstructed accordingly. Experimental results demonstrate the effectiveness of the proposed post-filters for two representative speech enhancement methods, namely the deep denoising autoencoder (DDAE) and the minimum mean-square-error (MMSE) spectral estimation methods.