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In this paper, hysteresis of magnetorheological (MR) fluids is identified from experimental tests following the mechanism of rate-independence and further studied to explore the hysteresis mechanism. The theoretical analysis based on the dipole model is provided to reveal the hysteresis mechanism of MR fluids. Specifically, the performance tests of a self-developed double-rod MR damper under different excitations show that instead of the typical force-velocity plot, the relationship between the force and displacement meets the requirements of rate-independence of the hysteresis well. A critical concept of "yield displacement" is defined and analyzed in the force-displacement plot to illustrate the hysteresis characteristics. In addition, the relationship of the normalized restoring force vs. strain is derived for a single chain from the dipole model. Then a stress-strain curve is developed for the multi-chain structure with an assumption of the dynamic equilibrium between the rupture and reconstruction of the chains. Sequentially, the hysteresis mechanism is established based on the force-displacement characteristics under reciprocating excitations. The consistency between the yield displacement in experiment and yield strain in theory verifies the effectiveness of the hypothetical hysteresis mechanism. The analysis results provide a guideline for the structural design of MR devices to enhance/reduce the hysteresis effect. The hysteresis mechanism-based further extension for the stress-strain properties of MR elastomers and the response time of MR fluids are provided as well.