Multiscale computing for heterogeneous materials provides a powerful and fidelity approach to handling situations where a suitable macroscopic constitutive model is unavailable. However, there have been very few instances in the industrial sector where concurrent multiscale modeling techniques have been adopted, primarily because they require significant computational resources. In particular, when dealing with large numbers of representative volume elements (RVEs) with different microstructure morphologies throughout the macrostructure. In this paper, the novelty lies in providing an artificial neural network (ANN) model-based multiscale approach for accelerating multiscale analysis of the elliptical inclusion-reinforced composites with spatially varying microstructures, which give up the assumption of global periodicity. To tackle this challenge, firstly, a series of RVEs with different microstructure morphologies characterized by inclusion orientations and aspect ratios, under different load conditions, are simulated to generate training data. Second, the back propagation neural network (BPNN) is trained offline using data acquired from the RVE simulation for learning the underlying and possibly RVE morphologies. The trained BPNN replaces the complex microscopic mechanical solution problems over each macroscopic integration point at each iteration, to update the macroscopic stress-strain responses and it significantly reduces the computational cost of multiscale simulations. Then, the trained neural network is implemented on ABAQUS via user-defined materials (UMAT) and its effectiveness is verified by comparison with the classical multiscale finite element method (FE2) method. Finally, the outstanding computational capability of the proposed approach is further demonstrated through two numerical examples.