This paper presents an emotion recognition system from clean and noisy speech. Geodesic distance was adopted to preserve the intrinsic geometry of emotional speech. Based on the geodesic distance estimation, an enhanced Lipschitz embedding was developed to embed the 64-dimensional acoustic features into a six-dimensional space. In order to avoid the problems brought by noise reduction, emotion recognition from noisy speech was performed directly. Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA) and feature selection by Sequential Forward Selection (SFS) with Support Vector Machine (SVM) were also included to compress acoustic features before classifying the emotional states of clean and noisy speech. Experimental results demonstrate that compared with other methods, the proposed system makes approximately 10% improvement. The performance of our system is also robust when speech data is corrupted by increasing noise.