In the application of optical imaging technologies to the biomedical field, the flexible optical cord is one of the key components used to deliver the reflected optical signal from the internal biological tissue to the biomedical imaging system. However, the conventional optical fibers suffer from a critical wiring limitation, which results in severe power losses under a small bending radius that is less than a few centimeters. In this paper, we demonstrate that holey optical fibers with 18 air holes in cladding have negligible bending loss under a minimum bending radius of 3 mm. Excellent bending insensitivity of the holey fibers can effectively reduce the device size and space, which will be highly beneficial to the flexible endoscopic common-path optical coherence tomography system. A curled optical cord, similar to a curled telephone cord, is specially designed and fabricated to accommodate access of the imaging probe to the biological target at flexible distances. The curled optical cord displays excellent optical properties of a much lower bending loss and better optical imaging quality, but the attenuation and insertion losses are still the same as that of a conventional single-mode fiber-based optical cord.