Recently, the smart grid has emerged as a promising technology to facilitate energy management by balancing the demand-supply curve. However, the intermittent nature of the distributed energy resources (DERs) causes uncertainties and nonlinearity in the smart grid environment which may greatly influence the energy planning, especially the generation and distribution. Therefore, energy load forecasting plays an important role to facilitate the operations in the smart grid. Though using traditional statistical and machine learning approach there exists a significant forecasting error and a high degree of overfitting. In recent years, deep neural network (DNN) architectures have been the focus of extensive attention, it shows superb ability to solve many complex problems in the field of computer vision and image processing. DNN provides a set of intelligent computational algorithms to solve the complicated nonlinear relationship between the input and output through multiple hidden layers. Therefore, we propose an energy load forecasting (ELF) model based on the deep neural network to manage the energy consumption in an efficient manner for smart grid applications. Specifically, this work presents the deep neural network architectures based on Deep Feed-forward Neural Network (Deep-FNN) and Deep Recurrent Neural Network (Deep-RNN) to forecast the hourly energy load. Both DNN architectures are trained with Levenberg-Marquardt training algorithm using different activation functions in the neurons of hidden layers. The proposed model is implemented on the aggregated electricity consumption dataset of the New York City. The forecasting error of both day-ahead and week-ahead forecasting demonstrate that the Deep-RNN with hyperbolic tangent activation function is better among all the test cases. Finally, the simulation results show that the proposed ELF model outperform the shallow neural network (SNN), ensemble tree bagger (ETB) and generalized linear regression (GLR).