We propose a new adaptive algorithm with decreasing step-size for stochastic approximations. The use of adaptive algorithm is widely spread in various applications across the fields such as system identification and adaptive control. We analyze the rate of convergence of the proposed algorithms. An averaging algorithm, on its optimality of the rate of convergence, is using to control the step sizes. Our proofs are based on recent results in stochastic approximations and Guass approximation Theorem.