A new double-heterostructure photonic crystal L3 microcavity is designed, under the condition of gentle confinement, the quality factor of the cavity is optimized to reach as high as 2.8105 by comparing the simulated mode distribution calculated by finite difference time domain algorithm with the ideal Gaussian distribution, while the mode volume remains small, Veff=0.1813(/n)3. This is the best result at present. Additionally, an energy correlation coefficient is introduced to qualitatively describe the optimization level of a photonic crystal microcavity, which improves the speed and the accuracy of optimization.