Taking both dipole and exchange interaction into aceount we have deduced the secular equation for the dipole-exchange spin waves in an axially magnetized cylin-drical ferromagnet. Numerical results of frequency spectra are also given. When the wave vector of the spin wave is small, dipole energy is the most important term and our results coincide with that of magnetostatic modes. When the wave vector becomes large, exchange energy plays a greatrole, and our results approach those of the theory of macroscopic exchange waves.