Periodic noise is a well-known problem in seismic exploration, caused by power lines, pump jacks, engine operation, or other interferences. It contaminates seismic data and affects subsequent processing and interpretation. The conventional methods to attenuate periodic noise are notch filtering and some model-based methods. However, these methods either simultaneously attenuate noise and seismic events around the same frequencies, or need expensive computation time. In this work, a new method is proposed to attenuate periodic noise based on sparse representation. We use a noise dictionary to sparsely represent periodic noise. The noise dictionary is constructed based on ambient noise. An advantage of our method is that it can automatically suppress monochromatic periodic noise, multitoned periodic noise and even periodic noise with complex waveforms without pre-known noise frequencies. In addition, the method does not result in any notches in the spectrum. Synthetic and field examples demonstrate that our method can effectively subtract periodic noise from raw seismic data without damaging the useful seismic signal.