The energy management (EM) of active distribution network (ADN) under uncertainties is a stochastic, nonconvex and nonlinear problem, which cannot be solved by traditional algorithms in acceptable time. In this paper, we decouple this computationally intractable problem into a series of subproblems which are easier to handle, and then solve them successively according to an improved approximate dynamic programming (IADP) algorithm. Different from the existing approximate dynamic programming (ADP) algorithms, which need to update value functions iteratively, IADP obtains approximate value functions directly using Galerkin method. Such that the time of updating approximate value functions can be omitted. Furthermore, the influence of each basis function on the approximate value function is evaluated according to the absolute value inequality principle. Then the unimportant basis functions are removed from the basis function set to speed up the algorithm. The historical data can also be embedded into IADP to facilitate the online decision-making and reduce the dependency of real-time forecast information. Numerical simulations on two modified IEEE test systems and a real 682-bus ADN are given to illustrate the effectiveness of the proposed approach.