In this paper, a dissipative soliton mode-locked fiber laser is established based on carbon nanotube in order to study the polarization dynamics of dissipative soliton by using a commercial polarimeter. Under the pump power of 160 mW, stable dissipatives soliton are observed to have a limited cycle polarization trajectory shown on Poincare sphere, indicating the periodic modulation of anisotropy in cavity. The stable dissipative soliton possesses a high signal noise ratio of 57.7 dB at fundamental frequency. Moreover, the fast oscillation of state of polarization leads to a lower degree of polarization (DOP). In addition, the polarization controllers are employed to compensate for the birefringence in the cavity to adjust the ratio between cavity length and birefringence length. As a result, we can observe the polarization evolving from the polarization locked attractor to the limited cycle attractor by adjusting polarization controllers. It is noted that this dynamic polarization trajectory can be manually controlled. By comparing polarization attractor with DOP, it is clear that the size of trajectory shown on Poincare sphere is inversely proportional to DOP. We expect our work to be conducible to studying the physics in lasers and creating a new type of polarization tunable laser.