The evaluation and analysis of the ecological vulnerability of urban green-space systems are conducive to the sustainable development of urban green-space systems. Taking the urban green-space system in the Beijing–Tianjin–Hebei region in 2010, 2015, and 2020 as the research object, an ESSR model was first constructed, and a total of ten types of impact factors were integrated into the four dimensions of “Exposure, Sensitivity, State and Response”. The weight of the impact factors was objectively determined via spatial principal component analysis, and the ecological vulnerability of the urban green-space system was evaluated via superposition analysis; the evaluation’s results were graded. Moreover, the transfer matrix, center-of-gravity migration model, standard deviation ellipse, and spatial autocorrelation analysis were used to study the temporal and spatial variation characteristics of the evaluation results; then, the driving force of impact factors was analyzed based on a geographical detector. Finally, the rationality of the evaluation results was verified using the changing trend of the remote sensing ecological index (RSEI). The results show that the ecological vulnerability of the urban green-space system in the Beijing–Tianjin–Hebei region has decreased year by year for the past ten years. The distribution law of “Hebei surrounds Beijing and Tianjin” is presented in this space, and 2015 is the mutation node. In 2010, the moderately and severely vulnerable areas of Hebei surrounded the mildly vulnerability areas of Beijing and Tianjin. Moreover, in 2015 and 2020, the mildly vulnerable areas of Hebei surrounded the severely vulnerable areas of Beijing and Tianjin. Vulnerability expands slightly in the east–west direction and shrinks slightly in the north–south direction, and the center of gravity shifts towards Beijing year by year along the northeast direction. Moreover, the spatial distribution of vulnerability shows significant positive spatial autocorrelations and exhibits very obvious agglomeration. In addition, vulnerability is the result of the combined effect of various factors, and education degree, human disturbance index, and annual average precipitation are the dominant factors. The analysis results provide a reference for the effective application and sustainable development of urban green-space ecological functions.