The estimation of head pose angle from face images is an integral component of face recognition systems, human computer interfaces and other human-centered computing applications. To determine the head pose, face images with varying pose angles can be considered to be lying on a smooth low-dimensional manifold in high-dimensional feature space. While manifold learning techniques capture the geometrical relationship between data points in the high-dimensional image feature space, the pose label information of the training data samples are neglected in the computation of these embeddings. In this paper, we propose a novel supervised approach to manifold-based non-linear dimensionality reduction for head pose estimation. The Biased Manifold Embedding (BME) framework is pivoted on the ideology of using the pose angle information of the face images to compute a biased neighborhood of each point in the feature space, before determining the low-dimensional embedding. The proposed BME approach is formulated as an extensible framework, and validated with the Isomap, Locally Linear Embedding (LLE) and Laplacian Eigenmaps techniques. A Generalized Regression Neural Network (GRNN) is used to learn the non-linear mapping, and linear multi-variate regression is finally applied on the lowdimensional space to obtain the pose angle. We tested this approach on face images of 24 individuals with pose angles varying from -90°to +90 °with a granularity of 2. The results showed substantial reduction in the error of pose angle estimation, and robustness to variations in feature spaces, dimensionality of embedding and other parameters.