Based on the vectorial Rayleigh-Sommerfeld diffraction integrals, the model for four-petal Gaussian beams propagating through an eccentric circular aperture is built. By choosing oblique optical axis as the reference optical axis and expanding the hard-edged circular aperture function as a finite sum of complex Gaussian functions, an analytical solution is performed. Furthermore, the detailed numerical calculation for the two-dimensional beams is presented. The simulation also shows that f parameters, beam order, location of aperture and truncation parameter affect the diffracted field, including location of center intensity and beam width. All these characteristics help us understand four-petal Gaussian beams propagation better.