This paper presents a distributed average consensus algorithm with least-mean-square deviation. The algorithm is designed to minimize the steady-state mean-square deviation in a network of nodes, where each node updates its value based on a weighted average of its neighbors' values, with additive noise. The problem is formulated as a convex optimization problem, allowing for efficient global solutions. The paper shows that the optimal edge weights can be found by solving a convex optimization problem, and compares the results with other weight design methods. The algorithm is applicable to various practical scenarios, including load balancing, coordination of autonomous agents, and network synchronization. The paper also provides several examples of graphs where the optimal edge weights are constant, and discusses the computational methods for solving the optimization problem. The results show that the proposed algorithm achieves a lower mean-square deviation compared to other methods, and is efficient in terms of computational cost.This paper presents a distributed average consensus algorithm with least-mean-square deviation. The algorithm is designed to minimize the steady-state mean-square deviation in a network of nodes, where each node updates its value based on a weighted average of its neighbors' values, with additive noise. The problem is formulated as a convex optimization problem, allowing for efficient global solutions. The paper shows that the optimal edge weights can be found by solving a convex optimization problem, and compares the results with other weight design methods. The algorithm is applicable to various practical scenarios, including load balancing, coordination of autonomous agents, and network synchronization. The paper also provides several examples of graphs where the optimal edge weights are constant, and discusses the computational methods for solving the optimization problem. The results show that the proposed algorithm achieves a lower mean-square deviation compared to other methods, and is efficient in terms of computational cost.