A modification of the Migdal-Kadanoff (MK) real-space renormalization technique is studied and applied to the q-state Potts model on the square and the simple cubic lattices. A parameter x which describes the boundary condition is introduced to the cluster-decimation (CD) approximation. When x=2, the present method is the same as the CD approximation, and in the limit x→∞ this method reduces to the MK technique. Critical temperatures and exponents of the Potts model are calculated for 0<q≤4 by using various boundary conditions. Very good estimates of critical properties are obtained. The choice of the boundary condition is discussed.