In neutrino experiments, neutrino energy reconstruction is crucial because neutrino oscillations and differential cross-sections are functions of neutrino energy. It is also challenging due to the complexity in the detector response and kinematics of final state particles. We propose a regression Convolutional Neural Network (CNN) based method to reconstruct electron neutrino energy and electron energy in the NOvA neutrino experiment. We demonstrate that with raw detector pixel inputs, a regression CNN can reconstruct event energy even with complicated final states involving lepton and hadrons. Compared with kinematics-based energy reconstruction, this method shows a significantly better energy resolution. The reconstructed to true energy ratio shows comparable or less dependence on true energy, hadronic energy fractions, and interaction modes. The regression CNN also shows smaller systematic uncertainties from the simulation of neutrino interactions. The proposed energy estimator provides improvements of $16\%$ and $12\%$ in RMS for $\nu_e$ CC and electron, respectively. This method can also be extended to solve other regression problems in HEP, taking over kinematics-based reconstruction tasks.