Immunodominance is a common phenomenon observed in multiple epitopes immune systems. Previous studies hypothesize that the competition among CD8+ T cell responses against different epitopes can be used to explain immunodominance. This paper proposes a mathematical model that describes the dynamics of CD8+ T cells primed by antigen-presenting dendritic cells (DCs) in the lymph nodes, and shows that the overall avidity of the interactions between peptide-specific T cells and cognate antigen-bearing DCs may determine the immunodominance. The model suggests the probability that a peptide-specific T cell be immunodominant is proportional to (1) the cognate T cell receptor (TCR) affinity, (2) the number of complexes of cognate peptide and major histocompatibility complex (pMHC) per DC, and (3) the half-life of cognate peptide-specific pMHC. The model predicts a threshold density of pMHC complexes for T cell activation. These observations from the mathematical model are consistent with experimental studies in the open literature. For DC-based vaccine design, the model suggests a strategy of immunotherapy based on the injection of cognate antigen-pulsed DCs.