We introduce Adaptive Procedural Task Generation (APT-Gen), an approach to progressively generate a sequence of tasks as curricula to facilitate reinforcement learning in hard-exploration problems. At the heart of our approach, a task generator learns to create tasks from a parameterized task space via a black-box procedural generation module. To enable curriculum learning in the absence of a direct indicator of learning progress, we propose to train the task generator by balancing the agent's performance in the generated tasks and the similarity to the target tasks. Through adversarial training, the task similarity is adaptively estimated by a task discriminator defined on the agent's experiences, allowing the generated tasks to approximate target tasks of unknown parameterization or outside of the predefined task space. Our experiments on the grid world and robotic manipulation task domains show that APT-Gen achieves substantially better performance than various existing baselines by generating suitable tasks of rich variations.