Diffusion-time (td) dependent diffusion MRI is a promising tool to probe tissue microstructure. Although different diffusion gradient waveforms (DGW) have been introduced to achieve short and long td’s, whether they have comparable sensitivity to microstructural changes remains to be investigated. Here, we examined the td-dependency of kurtosis measured using pulsed, bipolar, and oscillating gradients with different microstructural substrates. Simulations and in vivo experiments showed that the choice of DGW affects the characteristics of time-dependent kurtosis, and this effect varied with microstructural size and permeability. This knowledge is important for design of td-dependent diffusion MRI experiments.