The brain is targeted for processing temporal sequence information. It remains largely unclear how the brain learns to store and retrieve sequence memories. Here, we study how recurrent networks of binary neurons learn sequence attractors to store predefined pattern sequences and retrieve them robustly. We show that to store arbitrary pattern sequences, it is necessary for a recurrent network to include hidden neurons even though their role in displaying sequence memories is indirect. We develop a local learning algorithm to learn sequence attractors in recurrent networks with hidden neurons. The algorithm is proved to converge and produce sequence attractors. We demonstrate our model can store and retrieve sequences robustly on synthetic and real-world datasets. We hope that this study provides new insights in understanding temporal information processing in the brain.