Proof-of-work (PoW) is a consensus protocol that establishes consensus in a permissionless environment, allowing individuals to join or exit the protocol freely. PoW acts as a mechanism for selecting a leader from a network of participants (miners) to add the next block to the chain and assign a lucrative reward to honest miners by successfully solving a computationally challenging puzzle. However, in doing so, the PoW mining scheme puts a considerable computation load on the computing nodes, resulting in significant energy consumption and thereby increased carbon dioxide emissions. Hence, to reduce this energy inefficiency in the PoW consensus algorithm, we propose an Enhanced Green Proof-of-Work (EG-PoW) algorithm for blockchain. The presented algorithm uses and extends the concept of a very well-known Green-PoW algorithm. The given scheme divides time into epochs, where each comprises three mining rounds: in the first round, all network nodes can participate in the mining process, in the second round only runner(s)-up of a mining round can take part, whereas in the third and final round, only the winner of the first mining round gets the chance to mine in this round. This considerably reduces the number of competing nodes and overall energy consumption in the mining process.