Negative linear compressibility (NLC) is a rare and counterintuitive phenomenon because materials with this property would expand along one specific direction when uniformly compressed. NLC materials have a broad range of potential applications in designing pressure sensors, artificial muscles, and so on. Designing and searching for systems with NLC is desired and crucial for material and compression science. Herein, with the help of high-pressure X-ray diffraction measurements and density functional theory calculations, we find that the 2D layered Co(SCN)2(pyrazine)2 exhibits NLC with a new mechanism: layer sliding. When compressed, the ab planes slide along the a axis, leading to the decrease of lattice parameter β, which results in the NLC effect along principal axis X3 (≈ -0.84a - 0.55c). The layer sliding mechanism opens exciting opportunities for seeking, designing, and synthesizing new classes of materials with anomalous mechanical properties in monoclinic layered or other related systems.