We study the nonthermal emission of pulsar wind nebulae (PWNe) from radio to TeV γ-ray energies with a simplified time-dependent injection model. In this model, a relativistic wind of particles driven by a central pulsar with a spin-down power L(t) is blown into the ambient medium and a shock wave is formed, which accelerates the particles to very high energies through the Fermi acceleration mechanism in the PWN. The relativistic particles in the PWN therefore consist of two components, one coming directly from the pulsar magnetosphere and the other from shock acceleration in the PWN. The model PWN spectra follow a broken power law with different indices and a break energy Eb. The accelerated particles produce nonthermal photons through synchrotron radiation and inverse Compton scattering off soft photon fields. We apply this model to the Crab Nebula, the PWN in MSH 15-52, and HESS J1825-137, which have all been found to emit very high energy (VHE) photons. Our results indicate that (1) the observed data, ranging from radio to VHE γ-rays, for the Crab Nebula can be reproduced by this model, where the emission from radio to medium-energy γ-rays is from the synchrotron emission due to the injected electrons, whereas the high-energy photons primarily come from inverse Compton scattering of the high-energy electrons on synchrotron photons; and (2) the TeV emission from the PWN in MSH 15-52 and HESS J1825-137 mainly comes from the inverse Compton scattering of the high-energy electrons on infrared photons.