We present a linear-time elimination method to adaptively reduce the nine intraprediction modes in H.264/AVC to two, three, five, or nine modes while preserving a satisfactory reconstructed video quality. Resemblance between prediction modes and appearing frequency for each prediction mode are first determined in an off-line way from the training video sequences. Prediction modes are modeled as vertices and resemblance between two prediction modes as the weight of the connecting edge in a complete graph. Then, find the Hamilton cycle with the minimum sum of weights. When encoding each intrablock, prediction modes corresponding to the adjacent vertices along the Hamilton cycle are examined for similarity. The prediction mode which appears less frequently in a pair of similar prediction modes is declared as redundant and eliminated. When compared with Laroche et al.’s method which aims to reduce the bitrate, experimental results demonstrate that the proposed elimination method can substantially reduce the execution time while preserving the peak signal-to-noise ratio and bitrate performance.