This paper considers the question of the rate of convergence to α-stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to α-stable random variable where 1 < α < 2, in the generalized CLT, that is, for the partial sums of independent identically distributed random variables which are not assumed to be square integrable. This work is a technical report based on the Zolotarev paper in [1].