The exploitation of underground coal resources has stepped up local economic and social development significantly. However, it was inevitable that time-dependent surface settlement would occur above the mined-out voids. Subsidence associated with local geo-mining can last from several months to scores of years and can seriously impact infrastructure, city planning, and underground space utilization. This paper addresses the problems in predicting progressive residual surface subsidence. The subsidence process was divided into three phases: a duration period, a residual subsidence period, and a long-term subsidence period. Then, a novel mathematical model calculating surface progressive residual subsidence was proposed based on the logistic time function. After the duration period, the residual subsidence period was extrapolated according to the threshold of the surface sinking rate. The validation for the proposed model was estimated in light of observed in situ data. The results demonstrate that the logistic time function is an ideal time function reflecting surface subsidence features from downward movement, subsidence rate, and sinking acceleration. The surface residual subsidence coefficient, which plays a crucial role in calculating surface settling, varies directly with model parameters and inversely with time. The influence of the amount of in situ data on predicted values is pronounced. Observation time for surface subsidence must extend beyond the active period. Thus back-calculated parameters with in situ measurement data can be reliable. Conversely, the deviation between predictive values and field-based ones is significant. The conclusions in this study can guide the project design of surface subsidence measurement resulting from longwall coal operation. The study affords insights valuable to land reutilization, city planning, and stabilization estimation of foundation above an abandoned workface.