Under the excitations of the high-frequency and weak low-frequency signals, the effects of linear time delay feedback on the vibrational resonance in overdamped bistable system and Duffing systems are investigated respectively. Both the analytical and the numerical results show that the response amplitude of the system to the low-frequency signal varies periodically with the delay parameter simultaneously (with two different periods, i.e., the periods of the two exciting signals). Numerical results also indicate that the delay feedback can induce vibrational resonance in the monostable Duffing system in which there exists no traditional vibrational resonance. By adjusting the delay parameter, not only the vibrational resonance can be effectively controlled, but also the response of the system to the weak low-frequency signal can be further improved.