A case-cohort design is proposed as a means of reducing cost in large cohort studies. In modeling process, case-cohort studies can acquire more efficiency from taking parameter constraints into consideration. In this paper, we fit the Cox model with constraints to case-cohort data and develop an inverse probability weighted approach for regression analysis. We establish asymptotic properties by applying a Lagrangian approach based on Karush-Kuhn-Tucker conditions. We develop a constrained minorization-maximization algorithm for the implementation of the proposed estimator. Simulation studies are conducted to assess the finite-sample performance. A data example from a Wilms tumor study is analyzed to demonstrate the application of the proposed method.