We perform a theoretical investigation of the small-signal modulation characteristics of light-emitting diodes (LEDs) for visible light communication (VLC) applications. A comprehensive model for the small-signal frequency bandwidth is developed using a carrier rate equation with the ABC recombination model. Using the obtained general form of the 3-dB bandwidth (f3dB), we analyze the dependence of the bandwidth on various parameters of the LEDs. The internal quantum efficiency (IQE) is found to significantly influence the modulation bandwidth of LEDs. At a high current density, f3dB is approximately inversely proportional to IQE, suggesting the importance of a trade-off between high IQE and fast modulation speed. In addition, we analyze and discuss the effects of the radiative recombination coefficient, current density, and quantum-well thickness on f3dB, comparing the modeling results with previous experimental data. The presented model of the modulation bandwidth can be advantageous in understanding the modulation characteristics of LEDs for high-speed VLC.