In recent years, with the rapid advancement of China’s urbanization, the contradiction between urban development and the ecological environment has become increasingly prominent, and the urban ecological system now faces severe challenges. In this study, we proposed an ecological index-based approach to monitor and evaluate the ecological environment using a Google Earth Engine cloud-based platform and Landsat time series. Firstly, a long-term series of Landsat images was obtained to construct and calculate the remote sensing-based ecological index (RSEI). Then, the Theil–Sen median estimation and the Mann–Kendall test were used to evaluate the trend and significance of the RSEI time series and combined with the Hurst index to predict the future development trend of the ecological environment in the study area. Finally, the coefficient of variation method was used to determine the temporal stability of the ecological environment. Taking Zhoushan Archipelago, China, as the study area, we mapped the distribution of the ecological environment using a spatial resolution of 30 m and evaluated the ecological environment from 1985 to 2020. The results show that (1) from 1985 to 2020, the average RSEI in the Zhoushan Archipelago decreased from 0.7719 to 0.5817, increasing at a rate of −24.64%. (2) The changes in the areas of each level of ecological environmental quality show that the ecological environment in the Zhoushan Archipelago generally exhibited a decreasing trend. During the study period, the proportion of the areas with excellent ecological environmental quality decreased by 38.83%, while the proportion of areas with poor and relatively poor ecological environmental quality increased by 20.03%. (3) Based on the overall change trend, the degradation in the ecological environment in the Zhoushan Archipelago was greater than the improvement, with the degradation area accounting for 84.35% of the total area, the improvement area accounting for 12.61% of the total area, and the stable area accounting for 3.05% of the total area. (4) From the perspective of the sustainability of the changes, in 86.61% of the study area, the RSEI exhibited positive sustainability, indicating that the sustainability of the RSEI was relatively strong. (5) The coefficient of variation in the RSEI was concentrated in the range of 0–0.40, having an average value of 0.1627 and a standard deviation of 0.1467, indicating that the RSEI values in the Zhoushan Archipelago during the study period were concentrated, the interannual fluctuations of the data were small, and the time series was relatively stable. The results of this study provide theoretical methods and a decision-making basis for the dynamic monitoring and regional governance of the ecological environment in island areas.