Magnetorheological fluid (MRF) is a kind of intelligent material with magnetic field response properties, which can realize the rapid and reversible control of physical properties under the action of external magnetic field. The MRF composite column specimens with the magnetic regulation stiffness characteristics are prepared by filling and encapsulating MRF in hollow Ecoflex tubes; When a magnetic field is applied, the magnetic particles form chain or columnar structures along the direction of the magnetic field, which makes the MRF composite column exhibit the characteristics of magnetic hardening or stiffness enhancement. The critical loads of specimens with different lengths under different magnetic fields are investigated. First, the quasi-static compression experiment is conducted to measure the compressive load versus compressive displacement curves of the specimens, from which the critical loads were obtained. In order to describe the critical loads of the MRF composite columns under arbitrary magnetic fields, the compressive instability model is proposed based on the modification of Euler's formula. The model parameters are determined according to the experimental data of compressive instability, and the model fitting results show excellent agreement with the experimental data. This model can predict the potential performance of magnetically adjustable composite columns, thereby guiding structural optimization design and promoting their application as adjustable stiffness elements in metamaterial structure design, soft actuators, etc.