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We study the nonthermal emission of the Crab nebula in the bands from radio to TeV gamma-ray on a simplified time-dependent injection model. In this model, relativistic electrons in the Crab nebula consists of two components and their injected spectrum is a broken power law with different indices and a break energy. The relativistic elections emit nonthermal photons through synchrotron and inverse Compton scattering off soft photon fields inside the nebula. The resulting spectrum calculated with the model is well consistent with the observed data ranging from radio to very high energy gamma-rays for the Crab nebula, where the emission from radio to medium gamma-rays is from electron's synchrotron emission, whereas the emission above similar to 100 MeV primarily comes from the inverse Compton scattering of the relativistic electrons on synchrotron photons.