Off-axis reflective afocal optical systems have important applications in space telescopes. Freeform surfaces can correct the asymmetric aberrations in off-axis reflective afocal systems. It is very important to design the initial layouts of freeform off-axis reflective afocal systems. In this paper, an orthogonal seed curve extension (OSCE) algorithm was proposed to design the initial layouts of freeform off-axis reflective afocal systems directly. Off-axis afocal three-mirror and four-mirror systems with magnifications of 10 and 20, respectively, were designed to verify the feasibility of the method. The results show that the root-mean-square (RMS) wavefront error of the initial layout of the off-axis three-mirror system is 0.36 λ, and that of the off-axis four-mirror system is 0.18 λ. The RMS wavefront errors of the two initial layouts after optimization are both less than 0.02 λ.