In the current era, electricity demand has skyrocketed. Power grids have to face a lot of uneven power demand daily. During a certain period in a day, the power demand peaks, making it difficult for the grid to meet the demand. To deal with this problem, an intelligent Home Energy Management (HEM) can be beneficial. Smart HEM systems can schedule loads from peak to low peak hours. Thereby reducing peak load on the grid as well as reducing decreasing the costs incurred by a user. In this paper, we proposed a Deep Reinforcement Learning model with prioritized experience sampling (PQDN-DR) for appropriate demand response, and the problem of load shifting is simulated as a game. We also propose a novel reward system for better convergence of the DRL model to near-optimal strategies and a DR adapted Epsilon Greedy Policy to guide the agent in exploration phase for faster convergence. The proposed system minimizes power demand peak and consumers’ bills simultaneously. The proposed method has successfully reduced the peak load and peak costs in smaller DR environment. The agent reduced costs and overall variance of the load profile for all customers for 24 h in the standard DR environment.