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A new analytic algorithm for Lane-Emden equations is proposed in this paper. The proposed algorithm is obtained by using a new iterative method. The new iterative method is a hybrid of variational iteration method and the Adomian decomposition method and further refined by introducing a new correction functional. This new correction functional is obtained from the standard correction functional of variational iteration method by introducing an auxiliary parameter γ in it. Further, a sequence G n x , with suitably chosen support, is also introduced in the new correction functional. The algorithm is easy to implement and gives fairly accurate solutions. Several test examples are given establishing the accuracy and the efficiency of the algorithm.