The Channel Assignment Problem (CAP) is to assign a minimum number of channels to requested calls in a cellular radio system while satisfying certain constraints. It is proven to be NP-complete. Considering Sivarajan?s benchmark 21-cell system assignment problem, or the Philadelphia problem, the constraints and traffic demands are given, a lower bound of channels needed for this system is fixed, and many strategies have been provided to solve the problem. This paper presents a dynamic channel assignment algorithm consisting of three stages: 1) the determine-lower-bound cell regular interval assignment stage; 2) the greedy region assignment stage; and 3) the genetic algorithm assignment stage. Its performance is verified through the Philadelphia problem and achieves lower bound solutions on 11 of the 13 instances, which is comparable with existing algorithms [1, 2, 7]. The algorithm also has the advantage that it is able to find optimum solutions faster than approaches using neural-networks and simulated annealing.