A theory describing the light propagation in biconical PM- fiber with a birefringent crystal grown all-around the fiber waist is developed.One of the crystal refractive indexes is more than the fiber cladding one, therefore the fiber inside crystal does not guide the light with corresponding state of polarization. The efficiency of such a polarization filter is conditioned by the intensity of HE12 mode that is exited inside the taper with the polarization state slightly different from that of HE11 mode. This anisotropy results from HE11-HE12 coupling resonance splitting for alternative polarization states. Corresponding values of minimum HE11-HE12 propagation constants differences for two polarization states are not equal to each other as well. The theory is based on the second order perturbation method for coupled waves equations solution. The common relationship for polarizer Jones matrix is obtained and associated eigenvalues are studied. The polarizer extinction ratio as calculated depends on PM-fiber anisotropy axes orientation towards crystal axes, fiber polarization beat length and other fiber parameters. The extinction ratio for standard PM-fiber is shown to be in the range of 50-70 dB and can be improved by appropriate fiber anisotropy axes orientation.