We have numerically calculated amplitudes and wave forms of gravitational radiation emitted from a central core in an axisymmetric supernova. The rotational core collapse has been systematically simulated under the assumption that the dynamical system is axisymmetric, and the complex microphysics such as nuclear equation of state and electron capture are approximated by a phenomenological equation of state. We have utilized the quadrupole formula to calculate the amplitudes and the wave forms of gravitational wave, and we have also assumed the Newtonian evolution of hydrodynamics. From these computations we have obtained burst-type wave forms. It is found from the comparison with results by Müller et al. or by Finn that the peak amplitude is sensitive to the stiffness of equation of state around the core bounce. Our results also show that the duration of the first burst is simply determined from the mean density of the inner core at the core bounce. Since the mean density of the inner core at the core bounce is dependent upon the angular momentum of the inner core and the stiffness of matter, we find it possible to obtain the information as to the angular momentum of a stellar core and the equation of state of high-density matter from the combined data of amplitude and duration of the burst from axisymmetric supernova explosion.