The composition and basic experiments of sticker model and its realization process in basic biochemical experiments were analyzed. Sticker model was simplified to solve the maximum clique problem. In sticker model, DNA sequence detection method based on electrophoresis technology and separation experiment was put forward, which can be used to detect experimental results containing various memory chains. Based on separation experiment DNA algorithm of maximum clique problem and its biochemical realization process were put forward, first the initial solution space of all nonempty vertex subets was created, and all vertex subsets satisfying the requirement of nonadjacent were selected from the initial solution space to detect each edge doing separation experiment, so all cliques are obtained, then all maximum cliques are obtained by doing electrophoresis experiment. The validity and feasibility of the DNA algorithm are explained by a simulate experiment.