This paper presents a simple and fast approach to find a minimum sampling frequency for multi-band signals. Instead of neighbor and boundary conditions, constraints on the sampling frequency were derived by using the geometric approach. Reformulation of the minimum sampling determination problem by using geometric approach enables to represent the problem as a basic inequality problem. Recursive algorithm was proposed to solve the constraints on the minimum sampling frequency. The proposed method was verified through numerical simulations in terms of the minimum sampling frequency and the computational efficiency by using 2-band and 3-band signals. Although the results illustrated the valid minimum sampling frequencies for the multi-band signals, due to the increase in the number of iterations, optimization approaches were recommended in the solution of the constraints on the minimum sampling frequency.