<p>A Mathieu-van der Pol coupling model with-out and with dual time-delay control is proposed in the paper. For the delay free system, the equilibrium point and critical condition are analyzed, and the dynamics of the system are investigated for different parameter conditions. The bifurcation diagrams of the amplitude of the response with respect to the frequency and the amplitude of the parameter excitation are obtained, respectively, which show different bifurcation mechanism. The alternative quasi-periodic and periodic motions of the system can be found as the parametric frequency increases, and the similar varying trends occur as the amplitude of parametric excitation increases under the 1-to-1 parametric resonance condition. Under the 1-to-2 parametric resonance condition, the motion of the system experiences the quasi-periodic motion to periodic state, then to chaos through the period-doubling bifurcation as the amplitude of the parametric excitation increases. The phenomenon of the coexisting of the multiple solutions is found for certain parameter conditions. For the system with the displacement and velocity time delays, the multiple scale method is applied to derive the second-order approximate solution. The averaged equations are derived based on the solvable conditions. The amplitude-frequency response curves under two parametric resonance conditions are obtained, and the effects of system parameters including the displacement and velocity feedback gains, amplitude of parametric excitation and damping coefficient on the response are investigated. Rich dynamic behaviors of the system including saddle-node and Hopf bifurcations as well as the joint effects between the nonlinearities and time delays are investigated. The results can be helpful for the engineering problems.</p>