In this paper, a new cubic subgrid-scale (SGS) model is proposed to capture the rotation effect. Different from the conventional nonlinear model with second-order term, the new model contains a cubic term which is originated in the Reynolds stress closure. All the three model coefficients are determined dynamically using the Germano's identity. The model is examined in the rotating turbulent channel flow and the Taylor-Couette flow. Comparing with the linear model and the second-order model, the new model shows better performance.