Conventional energy harvester typically consists of a cantilevered composite piezoelectric beam which has a proof mass at its free end while its fixed end is mounted on a vibrating base structure. The resulting relative motion between the proof mass and the base structure produces a mechanical strain in the piezoelectric elements which is converted into electrical power by virtue of the direct piezoelectric effect. In this paper, the harvester is provided with a dynamic magnifier consisting of a spring-mass system which is placed between the fixed end of the piezoelectric beam and the vibrating base structure. The main function of the dynamic magnifier, as the name implies, is to magnify the strain experienced by the piezoelectric elements in order to amplify the electrical power output of the harvester. With proper selection of the design parameters of the magnifier, the harvested power can be significantly enhanced and the effective bandwidth of the harvester can be improved. The theory governing the operation of this class of cantilevered piezoelectric energy harvesters with dynamic magnifier (CPEHDM) is developed using the finite element method. Numerical examples are presented to illustrate the merits of the CPEHDM in comparison with the conventional piezoelectric energy harvesters (CPEH). The obtained results demonstrate the feasibility of the CPEHDM as a simple and effective means for enhancing the magnitude and spectral characteristics of CPEH.