Cohesive sediments erode as aggregate-by-aggregate at low bed shear stresses in flow. The behavior and mechanism of aggregate erosion are not well understood currently and therefore the erosion rate of aggregate erosion remains challenging to predict. In this study, the erosion process of aggregates during one turbulent bursting cycle is examined and a concept of the bursting pickup probability which denotes the possibility of an individual aggregate located in the bursting-affected bed area being entrained into flow by one occurrence of bursting is proposed. The bursting pickup probability is different from the pickup probability proposed by Einstein (1950) and the pickup probability proposed by Partheniades (1965) in both space and time scales. Based on the proposed bursting pickup probability and considering the average size of aggregates in the cohesive sediment bed and the erosion threshold of the bed, a formula for erosion rate of aggregate erosion of cohesive sediments is developed. The developed formula shows the degree of consolidation of sediments and the size distribution of the primary particles could affect the erosion rate through the erosion threshold. And the formula promises to be convenient for application, being based on the bed shear stress, the erosion threshold of the bed and the size distribution of the primary particles.