The dynamical behaviour of a Duffing-van der Pol oscillator under a class of linear-plus-nonlinear state feedback control with a time delay is investigated in this paper by means of the method of averaging. The two slow-flow equations on the amplitude and phase of response are siplified by truncating the Taylor expansions of those terms containing time deklay . It is shown that the stability of the trivial solution is only associated with the coefficients of linear terms, including the gains of linear feedback control, in the original system. Therefore the trivial solution can be stabilized by appreciate choice of gains and time delay of linear feedback, which indicates that limit cycles can be eliminated. Different from the case of the trivial solution, the amplitude of nontrivial solutions is also associated with the coefficients of nonlinear terms besides linear terms in the original systems. However, limit cycles may disappear through amplitudes being infinite or zero when control parameters are varied. It is noticeable that the effect of time delay in feedback control on dynamical systems is peridoc. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.