We report a novel technique for polarimetric characterization of samples through a flexible fiber endoscope, with a single shot measurement per pixel. The sample is simultaneously probed with a large diversity of polarization states, and both degree of polarization and linear retardance are determined thanks to specific processing of data. The probe polarization states are spectrally encoded on the 10 nm bandwidth of the source. The key component of the endoscope is a 3 m long specially designed optical fiber which consists of the optimized concatenation of highly birefringent fiber pieces. For a proof of principle, different calibrated or manufactured samples were successfully characterized. The proposed technique is attractive in view of reducing the measurement time of polarimetric images, in endoscopic applications.