Developing robustness methods is imperative to retaining good performance for automatic speech recognition (ASR)systems when being confronted with different environmental noise or channel distortion. Previous studies have pointed out that exploration of low-dimensional structures of speech features is beneficial to generating robust features so as to enhance ASR performance. Along this research direction, we argue that the intrinsic structures of speech features lying on a manifold subspace of low dimensionality residing in their original ambient space of high dimensionality. This way, noise components can be ruled out by projecting noisy speech features into the pre-learned subspace of manifold structures. This paper explores the intrinsic geometric low-dimensional manifold structures inherent speech features' modulation spectra, with the goal to generate speech features that are more robust to environmental noise and channel distortion. The key novelty of our work is two-fold: 1)we put forward an innovative use of the graph-regularization based method to generate robust speech features by preserving the inherent manifold structures of modulation spectra and excluding irrelevant ones, and 2)we also compare our approach with several mainstream methods that also explores low-dimensional structures of data instances with in-depth analysis. A comprehensive set of empirical experiments carried out on an ASR benchmark task seem to reveal the superior performance of our proposed methods.