Dynamical blebbing in an oil-water system is reported together with a quantitative analysis of interfacial deformation. An oil droplet containing a fatty acid that floats on an aqueous phase containing a cationic surfactant shows blebbing-type deformation at the oil-water interface. Such deformation is caused by an out-of-equilibrium concentration distribution across the interface. The generation and breakage of aggregates at the interface is associated with the time-dependent instability of the interface that accompanies the blebbing. In a quantitative analysis, the size of the bleb depended on the size of the oil droplet: the size of the bleb was inversely proportional to the square root of the radius of the oil droplet approximately. Furthermore, the experimental results showed that an oil droplet undergoes translational motion, i.e., active Brownian motion, under a suitable size of the oil droplet. A simple mathematical model based on the elasticity of the aggregates is proposed, and this agrees well with the experimental results.