Intensity fluctuation and phase noise are key factors limiting the applications of the diode lasers is many fields. The intensity noise of a free-running diode laser was investigated experimentally. Tens of longitudinal modes from the diode laser were successfully separated and identified by a self-made monochromator with 0.01 nm resolution. The noise of either the individual mode or the jointed modes of main mode and the sideband modes was detected using a low-noise radio frequency photodetector. The properties of the intensity noise between either the main mode and the side modes, or the side modes themselves were investigated systematically. The anticorrelation between main mode and side modes was confirmed, and the periodical anticorrelations between small longitudinal modes were found. These results can help us to understand the mechanism of the intensity noise of the diode lasers as well as the noise suppression for intensity-squeezed light generation.