Purely soft actuators often suffer from poor grasping stability, low load capacity, and non-adjustable stiffness. To address these limitations, this study presents a pneumatic variable-stiffness soft actuator enabled by a laterally arranged fiber-jamming layer. Under an externally applied vacuum (negative gauge pressure), the fiber contact network is compacted to realize reversible stiffness modulation through frictional fiber jamming, without relying on geometric/structural interlocking. This mechanism also alleviates typical drawbacks of existing jamming media, including crease defects in layer jamming and particle migration/loosening in granular jamming. Based on the principle of virtual work and a Hertzian contact assumption, analytical models are developed for actuator bending and equivalent stiffness. Bending, stiffness, comparative variable-stiffness, and object grasping experiments are conducted to validate the proposed design. The results show that, under random perturbations of the driving pressure (randomly varying within 50–60 kPa), the peak-to-peak fluctuation of the bending angle is reduced by 78% compared with a single actuating layer (pneumatic chambers only). When the jamming-layer gauge pressure decreases from 0 kPa to −80 kPa, the tip equivalent stiffness increases by 220.5%. Under matched structural dimensions and pressure ranges in a controlled benchmarking setup, the stiffness modulation range is improved by 25.24%, 59.44%, and 19.36% relative to layer-, granular-, and vertically aligned fiber-jamming actuators, respectively. Meanwhile, the repeatability index (RSD) is reduced by 20.64%, 41.85%, and 10.78%. These results demonstrate that the proposed actuator provides a large stiffness-tuning capability with good repeatability, thereby improving grasping stability.