Exploration in environments with sparse feedback remains a challenging research problem in reinforcement learning (RL). When the RL agent explores the environment randomly, it results in low exploration efficiency, especially in robotic manipulation tasks with high dimensional continuous state and action space. In this paper, we propose a novel method, called Augmented Curiosity-Driven Experience Replay (ACDER), which leverages (i) a new goal-oriented curiosity-driven exploration to encourage the agent to pursue novel and task-relevant states more purposefully and (ii) the dynamic initial states selection as an automatic exploratory curriculum to further improve the sample-efficiency. Our approach complements Hindsight Experience Replay (HER) by introducing a new way to pursue valuable states. Experiments conducted on four challenging robotic manipulation tasks with binary rewards, including Reach, Push, Pick&Place and Multi-step Push. The empirical results show that our proposed method significantly outperforms existing methods in the first three basic tasks and also achieves satisfactory performance in multi-step robotic task learning.