Local radiative density of optical states (LDOS) offers a tool to control the radiative rate of spontaneous emission from molecules, atoms, and quantum dots, which is proportional to LDOS. This paper presents that LDOS how to make the population of excited-state decay exponentially in time, and how these dynamics can be affected. By adopting the plane-wave expansion method, properties of an inverse-opal photonic crystal are studied with the help of photonic dispersion relations. Results in this paper show that the LDOS is radically modified in photonic crystal, and the rate of spontaneous emission can be described by the functions of position in the crystal and orientation of transition dipole moment.