As machine learning models become increasingly integrated into healthcare, structural inequities and social biases embedded in clinical data can be perpetuated or even amplified by data-driven models. In survival analysis, censoring and time dynamics can further add complexity to fair model development. Additionally, algorithmic fairness approaches often overlook disparities in cross-group rankings, e.g., high-risk Black patients may be ranked below lower-risk White patients who do not experience the event of mortality. Such misranking can reinforce biological essentialism and undermine equitable care. We propose a Fairness-Aware Survival Modeling (FASM), designed to mitigate algorithmic bias regarding both intra-group and cross-group risk rankings over time. Using breast cancer prognosis as a representative case and applying FASM to SEER breast cancer data, we show that FASM substantially improves fairness while preserving discrimination performance comparable to fairness-unaware survival models. Time-stratified evaluations show that FASM maintains stable fairness over a 10-year horizon, with the greatest improvements observed during the mid-term of follow-up. Our approach enables the development of survival models that prioritize both accuracy and equity in clinical decision-making, advancing fairness as a core principle in clinical care.