Gout is a form of crystal arthropathy where monosodium urate (MSU) crystals deposit and elicit inflammation in a joint. Diagnosis of gout relies on identification of MSU crystals under a compensated polarized light microscope (CPLM) in synovial fluid aspirated from the patient's joint. The detection of MSU crystals by optical microscopy is enhanced by their birefringent properties. However, CPLM partially suffers from the high-cost and bulkiness of conventional lens-based microscopy, and its relatively small field-of-view (FOV) limits the efficiency and accuracy of gout diagnosis. Here we present a lens-free polarized microscope which adopts a novel differential and angle-mismatched polarizing optical design achieving wide-field and high-resolution holographic imaging of birefringent objects with a color contrast similar to that of a standard CPLM. The performance of this computational polarization microscope is validated by imaging MSU crystals made from a gout patient's tophus and steroid crystals used as negative control. This lens-free polarized microscope, with its wide FOV (>20 mm(2)), cost-effectiveness and field-portability, can significantly improve the efficiency and accuracy of gout diagnosis, reduce costs, and can be deployed even at the point-of-care and in resource-limited clinical settings.