We derived a mathematical expression for the temporal evolution of the number of particles due to shear coagulation, covering the later stage by expanding the initial stage approximation to take into account the formation of floc structure. In the derivation, it is assumed that flocculation proceeds through binary collisions between identical fractal flocs. The capture efficiency between flocs is calculated on the basis of trajectory analysis, which is determined by viscous hydrodynamic interaction between flocs and van der Waals attractive forces between two primary particles located at colliding points of flocs. The validity of the derived equation was tested by a coagulation experiment using polystyrene sulfate latex particles under conditions of rapid coagulation. The experiment was carried out in a laminar Couette flow generated in the gap between two concentric cylinders. Careful and direct observation of flocculation under microscopy provided the data on the fractal dimension as well as the temporal evolution of number concentration of flocs. The measured rate of coagulation gradually increases in accordance with the formation of the fractal structure of flocs. This behavior agreed very well with the prediction based on the derived equation.