The linear k-epsilon-k(p) two-phase turbulence model is rather simple, but it cannot predict the anisotropic turbulence of strongly swirling gas-particle flows. The second-order moment, two-phase turbulence model can better predict strongly swirling flows, but it is rather complex. Hence, the algebraic Reynolds stress expressions are derived based on two-phase Reynolds stress equations, and then the nonlinear relationships of two-phase Reynolds stresses and two-phase velocity correlation with the strain rates are obtained. These relationships, together with the transport equations of gas and particle turbulent kinetic energy and the two-phase correlation turbulent kinetic energy constitute the nonlinear k-epsilon-k(p), turbulence model. The proposed model is applied to simulate swirling gas-particle flows. Predictions give the two-phase time-averaged velocities and Reynolds stresses. The prediction results are compared with phase Doppler particle anemometer (PDPA) measurements and those predicted using the second-order moment model. The results indicate that the nonlinear k-e-kp model has modeling capability nearly equal to that of the second-order moment model, but the former can save much computation time.