There are a large number of high-speed micrometeoroids in space. The collision between micrometeoroids and spacecraft in orbit will lead to orbit deviation, performance degradation, structural damage, or even failure. Due to the instability of the Halo orbit, the effects of micrometeoroid collisions on the dynamic evolution of the Halo orbit around the Sun-Earth L₂ point are studied in this paper. First, an orbital model around the Sun-Earth L₂ is established, and the initial conditions of the Halo orbit are constructed using the differential correction method. Based on the Grün micrometeoroid flux model, the number of collisions between micrometeoroids and spacecraft is calculated. The velocity variation caused by the collision is evaluated. Then, the Runge-Kutta algorithm is used to solve the orbital dynamic equations of the Halo orbit, and the evolution of orbit deviation caused by the collisions is studied. Besides, the state transition matrix method is used to analyze the evolution of the initial state deviation, which is then compared with the numerical integration method. Finally, based on the state transition matrix method, the dynamic responses caused by different magnitudes and directions of the velocity increments are analyzed. It was found that the results obtained by the state transition matrix in a short time are basically consistent with the numerical integration method, while the final deviation can be calculated from the initial deviation with only one matrix multiplication, which is highly efficiency. The results also showed that due to the inherent instability of the Halo orbit, the initial small micrometeoroid collisions would grow rapidly. This may lead to more control fuel consumption and ultimately affect the life of the spacecraft. In addition, the direction of velocity increments caused by micrometeoroid collision has an important effect on the deviation transmission.