Blockchain is a technology that is rapidly gaining prominence and finding applications in various sectors such as banking, supply chain, healthcare, and e-governance. The consensus algorithm employed in a blockchain network is crucial as it directly impacts the network's performance and security. Different consensus techniques exist, including Proof of Work (PoW), Proof of Stake (PoS), Robust Proof of Stake (RPoS), and Delegate Proof of Stake (DPoS), each with its own set of advantages and disadvantages. In this work, we propose a new consensus algorithm called Delegated Proof of Stake with Exponential Back-off (DPoSEB). DPoSEB utilizes a stake-based selection of delegates and employs an exponential back-off technique to mitigate collisions among nodes within the network. Each delegate is assigned a random sleep time, and the node with the shortest wake-up time is chosen to mine the block for that particular round. However, collisions among nodes can still occur. To provide a fair chance for each delegate node, collided nodes are assigned an exponential back-off time. We implement our proposed algorithm on an Ethereum-based private blockchain network. To evaluate the effectiveness of our proposed work, we compare it with existing consensus mechanisms such as PoS (version 2) and Delegated RPOS with downgrading (DDRPOS) using different scenarios in terms of transaction latency, waiting time, and fairness as evaluation metrics. The results reveal that DPoSEB performs better than POS and DDRPOS.