Triboelectric nanogenerators (TENG) can effectively generate electrical energy from the otherwise wasted mechanical energy in our environment. However, since vibration energy scavengers are usually driven at their resonant frequency, vibrating TENGs (VTENG) can provide maximized output power only within a few Hz of input frequencies. Here, we report tandem TENGs which are able to optimally scavenge abundant vibration energy under a wide band of input frequencies (tens of Hz and beyond). We first investigate the dynamic response of a single VTENG by parametric analyses (external forces, mass, stiffness, and gap distance) according to input frequencies. Based on coupled behavior, we complete a design protocol for a single VTENG, providing optimal power generation at a given frequency. Finally, we demonstrate a tandem system of resonant VTENGs, where maximum output power can be produced over a broad range of input frequencies between 15 and 40 Hz. It is expected that our design protocol enables optimal energy conversion for an individual TENG and that tandem design will be practically useful for consistently scavenging a wide band of vibration energy from environmental sources such as vehicles, wind, and waves.