Based on the generalized integral formula and the complex Gaussian expansion of the aperture function, an approximate analytical propagation formula for a Lorentz beam passing through a circular-apertured misaligned paraxial optical system is derived. The analytical propagation formula of a Lorentz beam through a unapertured misaligned paraxial optical system is treated as the special case of the general formula. As a numerical example, the propagation properties of a Lorentz beam through an apertured misaligned thin lens are investigated numerically. The results show that diffraction of different intensity, in other words, the radius of the circular aperture apparently influences on the distribution of the normalized light intensity of the diffracted beam and its propagation law.