Quantum sensing has been receiving researcher’s attention these years due to its ultrahigh sensitivity and precision. However, the bandwidth of the sensors may be low, thus limiting the scope of their practical applications. The low-bandwidth problem is conquered by feedback control methods, which are widely utilized in classic control fields. Based on a quantum harmonic oscillator model operating near the resonant point, the bandwidth and sensitivity of the quantum sensor are analyzed. The results give two important conclusions: (a) the bandwidth and sensitivity are two incompatible performance parameters of the sensor, so there must be a trade-off between bandwidth and sensitivity in practical applications; (b) the quantum white noise affects the signal to be detected in a non-white form due to the feedback control.