Two-dimensional depth-resolved Jones-matrix images of scattering biological tissues were measured with novel double-source double-detector polarization-sensitive optical coherence tomography (OCT). The Jones matrix can be determined in a single scan with this OCT system. The experimental results show that this system can be effectively applied to the measurement of soft tissues, which are less stable than hard tissues. Polarization parameters such as diattenuation, birefringence, and orientation of the fast axis can be extracted through decomposition of the measured Jones matrix. The Jones matrix of thermally treated porcine tendon showed a reduction of birefringence from thermal damage. The Jones matrices of porcine skin and bovine cartilage also revealed that the density and orientation of the collagen fibers in porcine skin and bovine cartilage are not distributed as uniformly as in porcine tendon. Birefringence is sensitive to changes in tissue because it is based on phase contrast.