A high-static-low-dynamic stiffness (HSLDS) vibration isolator based on a tunable nesting-type electromagnetic negative stiffness (NS) mechanism is presented. The stiffness characteristics of the HSLDS system can be tuned by regulating the current in the coil. When the current is zero, the HSLDS system may degenerate into a passive isolator. The distinctive features of this proposed isolation system are demonstrated from two aspects: 1) In contrast to passive isolators, the proposed isolator can further widen the bandwidth of vibration isolation and improve the isolation performance near the natural frequency of the passive system; and 2) compared with certain other electromagnetic isolation systems, the proposed system has a more compact structure, heavier load capacity, and higher NS-generating efficiency. The proposed electromagnetic NS mechanism consists of four permanent magnets and four coil windings. Analytical models of the electromagnetic force and the displacement transmissibility are established. To select an appropriate structural parameter for the prototype, the effects of geometric parameters on transmissibility are discussed from a theoretical viewpoint. The vibration isolation performance of the proposed isolator system is verified, and a tuning strategy is investigated through experiments.