The propagation characteristics of the off-axis ellipse vector beam (OEVB) are studied in this paper. The analytic expressions of the electric field and the intensity after OEVB propagating in free-space are derived. Numerical results indicate that the intensity distribution of OEVB is asymmetric and the intensity distribution after propagating is determined by propagation distance, dislocation displacement and ellipticity. In addition to expanding, the intensity distribution of OEVB tends to steady-state distribution finally and the dark core of vector beam disappears gradually during propagation. The major axis and minor axis of the ellipse intensity distribution in the steady-state are exchanged with each other as compared with in the initial plane. The results can help us to understand the dynamic propagation characteristics of the ellipse vector beam under the off-axis situation, and they can also guide the calibration of the ellipse vector beam in practice.