Distributed Hash Table (DHT) uses decentralized load balance algorithms which are based on virtual servers for participating in asymmetric peers. Require the participating peers to be asymmetric, there by introducing another load imbalance problem which is symmetric and promise no precise performance metrics. In this paper, an original symmetric load balancing algorithm for DHTs is introduced where the peers approximate the system state with histograms. Unlike other algorithms, proposed work guarantees analytical performance in terms of the load balance factor and high convergence rate. Through implementation using Java and SQL server, shown that proposal work performs better in terms of load balance factor with a comparable cost.