The stochastic resonance (SR) phenomenon for an underdamped bistable system with two kinds of velocity time-delays driven by multiplicative and additive noise is investigated. Applying small time-delay approximation, under detailed balance condition, the stationary probability for the system is obtained. The expression for the transition rates out of the two stable states and that for the output signal-to-noise ratio (SNR) of the system are deduced by virtue of two-state theory. Single-peak phenomenon appears when the SNR changes with the velocity time-delays. Traditional SR occurs on the curves of the SNR versus the strengths of the multiplicative and additive noise. A resonance peak takes place when the SNR varies with the damping coefficient. Moreover, it is found that the effects of the two kinds of time-delays and those of the two noises on the SNR are different. The non-monotonous effect of system parameters on the SNR is also investigated.