We report a bending-insensitive multi-core fiber (MCF) for lensless endoscopy imaging with modified fiber geometry that enables optimal light coupling in and out of the individual cores. In a previously reported bending insensitive MCF (twisted MCF), the cores are twisted along the length of the MCF allowing for the development of flexible thin imaging endoscopes with potential applications in dynamic and freely moving experiments. However, for such twisted MCFs the cores are seen to have an optimum coupling angle which is proportional to their radial distance from the center of the MCF. This brings coupling complexity and potentially degrades the endoscope imaging capabilities. In this study, we demonstrate that by introducing a small section (1 cm) at two ends of the MCF, where all the cores are straight and parallel to the optical axis one can rectify the above coupling and output light issues of the twisted MCF, enabling the development of bend-insensitive lensless endoscopes.