Transmission spectrum of a one-dimensional photonic crystal micro-cavity containing dispersive medium are calculated by use of the finite-difference time-domain method, and frequency shift of defect modes is investigated. In comparison with photonic crystal without dispersive medium inside micro-cavity, we find the frequency shift phenomenon of defect modes which results from the medium dispersion. And then, the dependence of frequency shift of defect modes on dispersive medium parameters such as strength of dispersive, damping coefficient and centre frequency is analyzed in detail. The result shows that the above parameters of dispersive medium determine the resonant frequency of the defect modes. The frequency of the defect modes can be significantly tuned by adjusting carefully the dispersive medium parameters. Such phenomenon can be used to tune the resonant frequency, which has a great potential for a new generation of optical components.