Tissue viscosity is correlated with tissue pathological changes and provides information for tissue characterization. In this study, we report an optical method to track continuous shear-wave propagation at centimeter depths in an optically turbid medium. Shear-wave attenuation coefficients were measured at multiple frequencies using shear-wave laser speckle contrast analysis (SW-LASCA) to quantitatively estimate tissue viscosity using the Voigt model. Shear waves were generated within tissue-mimicking phantoms by an amplitude-modulated ultrasound (modulation frequency: 100 to 600 Hz) and tracked by time-resolved laser speckle contrast difference received on a charged-coupled device camera. Averaged contrast difference over a selected time window was related to shear-wave amplitude and used to calculate the shear-wave attenuation coefficient. Phantoms of varying viscosities (0.1 and 0.3 Pa s) were studied. Attenuation coefficients for different shear-wave frequencies (100 to 600 Hz) were calculated. Derived viscosity values had a maximum standard deviation of 9%, and these values were consistent with the independent measurements reported in a previous study using nonoptical methods.