Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and four-parameter logistic models (i.e., M3PL and M4PL). To address this issue, we propose an importance-weighted sampling enhanced Variational Autoencoder (VAE) approach for the estimation of M3PL and M4PL. The key idea is to adopt a variational inference procedure in machine learning literature to approximate the intractable marginal likelihood, and further use importance-weighted samples to boost the trained VAE with a better log-likelihood approximation. Simulation studies are conducted to demonstrate the computational efficiency and scalability of the new algorithm in comparison to the popular alternative algorithms, i.e., Monte Carlo EM and Metropolis-Hastings Robbins-Monro methods. The good performance of the proposed method is also illustrated by a NAEP multistage testing data set.