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The new medical Ti-14Mo-2.1Ta-0.9Nb-7Zr alloy was prepared by powder metallurgy. The high temperature compression behavior and the dynamic recrystallization behavior of the alloy were investigated by hot compression tests. The tests were performed with a Gleeble-1500D simulator at 780-960℃ and stain rate of 0.001-1s^-1 up to a deformation of 60%.The hyperbolic sine modified Arrhenius model, which included deformation activation energy <i>Q</i> and temperature <i>T</i>, was used to describe the hot compression deformation equation of maximum deformation resistance; and the material parameter function of <i>α</i>(<i>ε</i>), <i> n</i>(<i>ε</i>), <i>Q</i>(<i>ε</i>) and<i> A</i>(<i>ε</i>), was introduced to obtain the constitutive equations. The results show that the flow stress values predicted by the proposed model have a good agreement with experimental results, high value of correlation coefficient (<i>R</i>=0.99430) and low value of average absolute relative error (5.327%); the critical stress and critical stain for dynamic recrystallization (DRX) under different deformation conditions are accurately calculated based on the method of work hardening rate and the inflection points, which are determined by fitting a third order polynomial to the <i>θ-&#963;</i> and ln<i>θ-ε</i> curves. Then the mathematical models of critical stress <i>versus Z</i> parameter and the critical stress equations of dynamic recrystallization are deduced, the critical strain <i>ε</i>_c mainly concentrates in the 0.01-0.04 and the critical strains of dynamic recrystallization alloy under different deformation conditions change in tiny.