To resolve the deteriorated vibration isolation performance of existing passive quasi-zero stiffness (QZS) vibration isolators caused by time-varying loads and stiffness mismatch, this paper proposes a novel load-adaptive QZS vibration isolator (LAQVI) based on radial basis function (RBF) neural network adaptive sliding mode control (SMC). The isolator adopts a composite structure coupling linear springs and electromagnetic units, which delivers adjustable QZS characteristics based on a nonlinear stiffness compensation mechanism. This paper analyzes the influence of various key parameters on the QZS characteristics. Dynamic equation analysis clarifies the relationship between load mismatch and displacement transmissibility, and theoretical studies confirm that excitation current control effectively enhances isolation performance. In addition, a sliding mode controller based on RBF neural network adaptation is designed, leveraging the RBF neural network’s learning and adaptive capabilities for rapid load variation estimation. Simulation results show that the adaptive control of excitation current can effectively compensate for the deviation of the isolation platform and enhance vibration isolation performance. Finally, static experiments verify the QZS characteristics of the isolator, and dynamic load experiments demonstrate the controller’s adaptive adjustment ability for load changes. Vibration test results show that the LAQVI exhibits reliable load adaptability and effective low-frequency vibration isolation performance under time-varying load conditions. The proposed LAQVI provides a theoretical basis for the application of QZS vibration isolators in fields such as intelligent equipment.