Variable stiffness (VS) has revolutionized miniature surgical instruments, including cardiovascular catheters for minimally invasive surgeries (MISs), enabling advanced capabilities in stiffness modulation and multi-curvature bending. However, existing VS catheters with phase-changing materials are slow in softening and stiffening rates (≈90 s), which can lead to substantial increase in surgery duration. To address the slow stiffness change, we propose a VS catheter based on fiber jamming (FJ) that achieves instant stiffness changes (≤300 ms), enabling seamless catheter operations without delays. Moreover, our catheter, incorporating hundreds of ultrathin fibers into a slender 2.3-mm catheter body, achieves up to 6.5-fold stiffness changes. With adequate stiffness change, our twosegment catheter achieves complex bending profiles within seconds. In addition, the FJ-based design does not require electric currents or heating inside the human body, minimizing patient risks. This FJ-based VS catheter, with instantaneous response, adequate stiffness change, and enhanced safety, can potentially establish benchmarks in MIS, allowing medical practitioners to effectively address formidable diseases.