Recently, energy demand forecasting has emerged as a signi cant area of researchbecause of its prominent impact on greenhouse gases (GHGs) emissionand global warming.The problems of load forecasting are characterized by complexand nonlinear nature and also long-term historical dependency. Up to now,several approaches from statistical to computational intelligent have been appliedin this research led. The literature agrees with the fact that deep learningapproach is more capable in dealing with these characteristics among existingapproaches. However, the recent state-of-the-art deep network models are notrobust against dierent historical dependency. In this study, we propose a graphframework based on parallel DeepNet branches to tackle this challenge. Thisframework consists of multi parallel branches in which dierent kind of networkscan be incorporated. The parallel recurrent branches represent the historical dependencyof determinants individually and this leads to better performance incase of dierent historical dependency in data. In this case study, the performanceof the proposed model is examined through a comparison study withthe state-of-the-art deep network models. The comparison resulted in that theproposed framework can improve the load forecasting by a signi cant marginon average.