Chaotic laser has attracted much attention in the laser field in recent years and there is a wide range of applications in optical secure communication, chaos lidar, optical fiber sensing and biomedicine because of their advantages such as strong randomness and anti-interference, noise-like time series and δ-like autocorrelation function. The measurement resolution and sensing accuracy of chaotic laser are directly affected by the nonlinear characteristics of fiber laser, among which the polarization characteristics of the laser are very important for the practical application and basic research of laser. However, the laser stimulated photon and the excited photon have the same frequency, direction, phase and polarization because of its stimulated radiation. Therefore, the laser polarization characteristics will be affected by the laser gain medium, internal structure and other factors. However, in recent years, most researchers have only studied laser polarization characteristics for solving specific technologies, focusing on the detection, control of laser polarization and the polarization dynamics of vector solitons, instead of analyzing the change and regularity of laser polarization characteristics from the internal optical path of the system. The dynamic characteristics of output polarization components of chaotic fiber lasers are rarely discussed. In practical applications, optical nonlinear effect and fiber strain have certain influence on the polarization characteristics of laser. So, the output dynamic characteristics of the polarization component of chaotic fiber lasers are studied in detail in this paper.The chaotic laser is generated based on the nonlinear Kerr effect with an erbium-doped fiber ring laser (EDFRL), and the dynamics of the polarization components of the chaotic laser is experimentally studied by adjusting the pump current and the polarization. The output power, dynamic evolution, correlation and spectral characteristics of the polarization components of the chaotic fiber lasers are analyzed in detail. In the experiment, the output of EDFRL is monitored in real time by autocorrelation function.The power of chaotic fiber laser and its polarization component is linear with the pump current. The periodic, chaotic output and self-pulse of the polarization component are observed as the pump current increases, which is consistent with the dynamic evolution of the chaotic laser. The same dynamic evolution can be observed by changing the polarization state of the chaotic fiber laser. The correlation of polarization components is closely related to the output state of the system. In the experiment, the spectrum of different pump currents is analyzed. The shape of the spectrum does not change with the output state of the laser, and their central wavelength is almost unchanged.The results can provide a new idea for studying a novel polarization-controllable fiber lasers and multi-channel fiber sensing applications. The work is important for exploring the nonlinear dynamics of the polarization components of chaotic fiber lasers.