We investigate nonradial oscillations of a boson star by taking into account the emission of the gravitational waves in the framework of general relativity. Since only even-parity modes of perturbations couple to the gravitational waves, we analyze these modes. We solve the linearized perturbed equations for l=2 modes and find that there exist new types of quasinormal modes of boson stars. Contrary to the behavior of quasinormal modes of compact fluid stars, the imaginary part of the frequencies of the normal modes of boson stars are large, which implies a short damping time scale of oscillations.