Phase field crystal method is used to investigate the deformation process and mechanism of twined structure of a trigonal phase under uniaxial tensile deformation, and the evolution and corresponding micro-mechanism of low-angle symmetric and asymmetric grain boundaries (GB) as well as high-angle symmetric and asymmetric GB during deformation process are analyzed in detail. The deformation is performed under the condition that the direction of applied stress is parallel to that of initial GB. Results show that low-angle symmetric GB is composed of two kinds of edge dislocations with the angle made by Burgers vectors being around 60 During deformation, two kinds of dislocations in low-angle symmetric GB move along two opposite directions, then meet with the same kind of dislocation emitted from another GB leading to the annihilation of partial dislocations. As to the low-angle asymmetric GB, its only one kind of dislocation first climbs and moves along the horizontal direction of the applied stress, then each dislocation will break down into two dislocations with their Burgers vectors making an angle about 120, finally a perfect single crystal is formed via the movement and annihilation of dislocations. High-angle GBs first keep horizontal shape under the applied stress, then become serrated, and the dislocations are emitted from the cusps in GBs. Finally, the high-angle asymmetric GB will decompose with the movement and annihilation of dislocation, while the shape of high-angle symmetric GB becomes horizontal again. It can be seen that the high-angle symmetric GB is more stable than the high-angle asymmetric GB; this is in agreement with the results of experiments and molecular dynamics.