Diffusion-magnetic resonance elastography (dMRE) can acquire diffusion and mechanical properties simultaneously. However, intravoxel phase dispersion (IVPD) interferes with the calculation of the apparent diffusion coefficient (ADC). This study presents an approach to dMRE that reduces the influence of IVPD by introducing a new pulse sequence. The ADC and stiffness, obtained using the existing and proposed dMRE techniques, were compared with spin-echo (SE)-diffusion and SE-MRE, for a phantom. In existing dMRE technique, the ADC was changed by IVPD but that of proposed dMRE technique was unchanged. The results demonstrate that our dMRE technique is a robust method for addressing the IVPD.