The laser ultrasonic technique (LUT) has many advantages in dealing with the anisotropy of organic-rich shale over the transducer ultrasonic contacting measurement. We have developed a systematic procedure to estimate anisotropic parameter and elastic parameter in organic-rich shale from LUT measurement. A novel filtering method called the structural-oriented space-varying median filter (SOSVMF) is proposed for removing the erratic noise from the recorded data. We apply the proposed algorithm onto one synthetic example and real recorded data in artificial bakelite and organic-rich shale by using LUT to show the successful performance. Compared with the original recorded data, the denoised waveform by SOSVMF will also help to obtain more accurate parameter estimations of the anisotropic parameter and elastic parameter . More importantly, the presented systematic procedure may extend the application of LUT to the study of attenuation anisotropy in organic-rich shale and scale physical modeling. In addition, the surface-modification method may be an effective method to enhance the laser-ultrasonic conversion efficiency.