An analysis of the cylindical brush of an isolated comb copolymer molecule consisting of a semiflexible backbone and flexible side chains is presented. Using the Alexander-de Gennes approximation, we calculate the free energy of both straight and bent cylindrical brush and the brush persistence length lambda, and show that lambda scales as a function of the side chain length M as lambda proportional to M-2. The discrepancy between the asymptotic scaling behavior and recent computer simulation results is also discussed.