The Extreme Learning Machine (ELM) is an effective learning algorithm for a Single-Layer Feedforward Network (SLFN). It performs well in managing some problems due to its fast learning speed. However, in practical applications, its performance might be affected by the noise in the training data. To tackle the noise issue, we propose a novel heterogeneous ensemble of ELMs in this article. Specifically, the correntropy is used to achieve insensitive performance to outliers, while implementing Negative Correlation Learning (NCL) to enhance diversity among the ensemble. The proposed Heterogeneous Ensemble of ELMs (HE ${}^{\mathrm{2}}$LM) for classification has different ELM algorithms including the Regularized ELM (RELM), the Kernel ELM (KELM), and the $L_{\mathrm{2}}$-norm-optimized ELM (ELML2). The ensemble is constructed by training a randomly selected ELM classifier on a subset of the training data selected through random resampling. Then, the class label of unseen data is predicted using a maximum weighted sum approach. After splitting the training data into subsets, the proposed HE ${}^{\mathrm{2}}$LM is tested through classification and regression tasks on real-world benchmark datasets and synthetic datasets. Hence, the simulation results show that compared with other algorithms, our proposed method can achieve higher prediction accuracy, better generalization, and less sensitivity to outliers.