Inspired by the tremendous achievements of meta-learning in various fields, this paper proposes the local quadratic embedding learning (LQEL) algorithm for regression problems based on metric learning and neural networks (NNs). First, Mahalanobis metric learning is improved by optimizing the global consistency of the metrics between instances in the input and output space. Then, we further prove that the improved metric learning problem is equivalent to a convex programming problem by relaxing the constraints. Based on the hypothesis of local quadratic interpolation, the algorithm introduces two lightweight NNs; one is used to learn the coefficient matrix in the local quadratic model, and the other is implemented for weight assignment for the prediction results obtained from different local neighbors. Finally, the two sub-models are embedded in a unified regression framework, and the parameters are learned by means of a stochastic gradient descent (SGD) algorithm. The proposed algorithm can make full use of the information implied in target labels to find more reliable reference instances. Moreover, it prevents the model degradation caused by sensor drift and unmeasurable variables by modeling variable differences with the LQEL algorithm. Simulation results on multiple benchmark datasets and two practical industrial applications show that the proposed method outperforms several popular regression methods.