This article introduces a parallel-guided compliant mechanism, which can achieve a high stiffness ratio (maximum over minimum) of 75 times through pneumatic actuated layer jamming. The compliant mechanism is composed of two flexible beams sandwiched with thin plastic friction layers. With a novel beam cross-section, the beams have large thickness, but still retain high flexibility. The effect of layer jamming is augmented by this large thickness due to the increased leverage of friction force. The beams in parallel-guided configuration have higher vertical and torsional stability compared to a single beam setup. The functionalities of the compliant mechanism have been validated experimentally: stiffness is measured as a function of the applied vacuum pressure. This paper describes the design concept, FEA validation of the design concept, prototyping, experiment results, analytical model, and analysis of vertical and torsional stability. The proposed concept of the compliant mechanism provides a potential solution for design of variable stiffness robotic links for addressing safety concerns in physical human robot interaction. The analytical model for identifying critical design parameters for maximum stiffness-variation effect provides a guideline for high stiffness-variation design on similar structures.