Abstract: The sparse representation based on overcomplete dictionary is a new signal representation theory. Recent activities in this field concentrate mainly on the study of dictionary design algorithm and sparse decomposition algorithm. In this paper, a novel speech signal sparse representation algorithm is proposed based on adaptive overcomplete dictionary. Considering stationary signal with autocorrelation function of exponential decay, an adaptive overcomplete dictionary is constructed in terms of the Karhunen-Love (K-L) expansion. Furthermore, an effective algorithm based on the nonlinear approximation is proposed to obtain sparse decomposition of signal with the adaptive dictionary. The experimental results indicate that short-term stationary speech signal sparse representation based on the adaptability and algebraic structure of atom in the overcomplete dictionary has higher sparsity and better reconstructive precision. The sparse representation algorithm can preferably be used in compressed sensing.