Solving real-world sequential manipulation tasks requires robots to have a repertoire of skills applicable to a wide range of circumstances. To acquire such skills using data-driven approaches, we need massive and diverse training data which is often labor-intensive and non-trivial to collect and curate. In this work, we introduce Active Task Randomization (ATR), an approach that learns visuomotor skills for sequential manipulation by automatically creating feasible and novel tasks in simulation. During training, our approach procedurally generates tasks using a graph-based task parameterization. To adaptively estimate the feasibility and novelty of sampled tasks, we develop a relational neural network that maps each task parameter into a compact embedding. We demonstrate that our approach can automatically create suitable tasks for efficiently training the skill policies to handle diverse scenarios with a variety of objects. We evaluate our method on simulated and real-world sequential manipulation tasks by composing the learned skills using a task planner. Compared to baseline methods, the skills learned using our approach consistently achieve better success rates.