An analytical technique based on the Mueller matrix method and the Stokes parameters is proposed for extracting five effective parameters on the principal axis angle, phase retardance, diattenuation axis angle, diattenuation and optical rotation angle of anisotropic optical materials. The linear birefringence (LB) / circular birefringence (CB) properties and linear diattenuation (LD) properties are decoupled within the analytical model. The analytical method is then integrated with a genetic algorithm to extract the optical properties of samples with linear birefringence property using a fiber-based Polarimeter. The result demonstrates the feasibility of analytical model in characterizing five effective parameters of anisotropic optical material. Also, it confirms that the proposed fiber-based Polarimeter provides a simple alternative to existing fiber-based probes for parameter measurement in the near field or the remote environment. A low birefringence fiber-based Polarimeter based on effective parameters and genetic algorithm without using a fiber polarization controller is first proposed confirmatively.