Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Monte Carlo (MCMC) methods using a machine learning model. With latent generative models, SLMC methods realize efficient Monte Carlo updates with less autocorrelation. However, SLMC methods are difficult to directly apply to multimodal distributions for which training data are difficult to obtain. To solve the limitation, we propose parallel adaptive annealing, which makes SLMC methods directly apply to multimodal distributions with a gradually trained proposal while annealing target distribution. Parallel adaptive annealing is based on (i) sequential learning with annealing to inherit and update the model parameters, (ii) adaptive annealing to automatically detect under-learning, and (iii) parallel annealing to mitigate mode collapse of proposal models. We also propose VAE-SLMC method which utilizes a variational autoencoder (VAE) as a proposal of SLMC to make efficient parallel proposals independent of any previous state using recently clarified quantitative properties of VAE. Experiments validate that our method can proficiently obtain accurate samples from multiple multimodal toy distributions and practical multimodal posterior distributions, which is difficult to achieve with the existing SLMC methods.