Microwave radiation in several gigahertz frequency band is a common phenomenon in laser-plasma interactions. It can last hundreds of nanoseconds and cause huge electromagnetic pulse disturbances to electrical devices in experiments. It has been found that the microwave radiation might originate from the oscillation of charged chambers, the return current on target holders, the dipole radiation, the quadrupole radiation, and the electron bunch emitted from the plasma to the vacuum. The microwave radiation waveform, frequency spectrum, and intensity depend on many factors such as laser pulse, target, and chamber parameter. To distinguish the microwave radiation mechanisms, the influence of the experimental parameters on the radiation characteristics should be investigated systematically. In this paper we investigate the microwave radiation influenced by the laser intensity in nanosecond laser-plasma interactions. It is found that the microwave radiation intensity varies nonmonotonically with the laser intensity. For the lower laser intensity, the radiation intensity first increases and then decreases with laser intensity increasing, the radiation field continuously oscillates in tens of nanoseconds, and the radiation spectrum contains two components below and above 0.3 GHz, respectively. For the higher laser intensity, the radiation intensity increases with the laser intensity increasing, the radiation field has a unipolar radiation lasting tens of nanoseconds, and the radiation spectrum mainly includes the component below 0.3 GHz. The waveform and spectrum analysis show that these phenomena are due to the difference of the radiation mechanisms at different laser intensities. The frequency component below and above 0.3 GHz are induced by the electron bunch emitted from the plasma to the vacuum and the dipole radiation respectively. At low laser intensity, both the dipole radiation and the electron bunch emitted from the plasma contribute to the microwave radiation. At high laser intensity, the microwave radiation is mainly produced by the electron beam emitted from the plasma to the vacuum. This work is significant for understanding the microwave radiation mechanisms in nanosecond laser-plasma interactions, and implies the potential to provide a reference to the diagnosing of the escape electrons and the sheath field on the target surface by the microwave radiation in laser-plasma interaction.