The axiparabola is a novel reflective element proposed in recent years, which can generate a long focal line with high peak intensity, and has important applications in laser plasma accelerators. The off-axis design of an axiparabola has the advantage of separating the focus from incident rays. However, an off-axis axiparabola designed by the current method always produces a curved focal line. In this paper, we propose a new method to design its surface by combining geometric optics design and diffraction optics correction, which can effectively convert a curved focal line into a straight foal line. We reveal that the geometric optics design inevitably introduces an inclined wavefront, which leads to the bending of the focal line. To compensate for the tilt wavefront, we use an annealing algorithm to further correct the surface through diffraction integral operation. We also carry out numerical simulation verification based on scalar diffraction theory, which proves that the surface of this off-axis mirror designed by this method can always obtain a straight focal line. This new method has wide applicability in an axiparabola with any off-axis angle.