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COVID-19 prognosis using clinical tabular data faces significant challenges due to missing values and class imbalance issues. Existing methods often overlook the complex high-order interrelationship among clinicalattributes and struggle with training stability on imbalanced datasets. We propose ACGM, an attribute-centric graph modeling network that simultaneously addresses missing data imputation and COVID-19 prognosis. ACGM consists of three key modules: an attributes preprocessing module (APM) for coarse-grained imputation initialization, a graph-enhanced attributes imputation module (GEAIM) that models high-order inter-attribute relationships through graph structures, and a graph-enhanced disease prognosis module (GEDPM) that leverages these complex attribute interactions for final prediction. GEAIM and GEDPM employ a mean-teacher strategy with attributes graph matching to preserve high-order relationships, enhance training stability, and maintain structural integrity of attribute interactions. Extensive experiments are conducted on four public COVID-19 tabular datasets, demonstrating the superiority of our ACGM over existing methods. Through comprehensive interpretability analysis, we identify that attributes such as LDH, Difficulty In Breathing, and SaO2 significantly impact COVID-19 prognosis, aligning well with clinical insights and radiologist assessments.