We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurementmodified decay rates of the excited state. In the cases with frequent ideal measurements at zerotemperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature 405, 546 (2000)). The correction to the ideal decay rate is also obtained under the nonideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.