We propose a one-dimensional sandpile model with avalanche probability.The simulation is performed with the cellular automata method.As the local slope closes to the critical slope sands avalanche with a probability.The avalanche size and the average local slope are studied at different avalanche probabilities. The self-organized critical (SOC) behavior is studied at critical exponent α=1.50±0.02 as the avalanche probability is between 0.05 and 0.98.The average local slope descends with the increase of collapse probability.A sharp transition occurs between the trival behavior and SOC behavior in this model.The SOC phenomenon in one-demensional rice-pile experiment is well explained.