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Monitoring survival in cancer is a common concern for patients, physicians, and public health researchers. The traditional cohort approach for monitoring cancer prognosis has a timeliness problem. In this paper, we propose a survivorship-period-cohort (SPC) model for examining the effects of survivorship, period, and year-of-diagnosis cohort on cancer prognosis and for predicting future trends in cancer survival. We used the developed SPC model to evaluate the relative survival (RS) of patients with liver cancer in Taiwan (diagnosed from 1997 to 2016) and to predict future trends in RS by imputing incomplete follow-up data for recently diagnosed patient cohorts. We used cross-validation to select the extrapolation method and bootstrapping to estimate the 95% confidence interval for RS. We found that 5-year cumulative RS increased for both men and women with liver cancer diagnosed after 2003. For patients diagnosed before 2010, the 5-year cumulative RS rate for men was lower than that for women; thereafter, the rates were better for men than for women. The SPC model can help elucidate the effects of survivorship, period, and year-of-diagnosis cohort effects on cancer prognosis. Moreover, the SPC model can be used to monitor cancer prognosis in real time and predict future trends; thus, we recommend its use.