The application of intravoxel incoherent motion (IVIM) and diffusion kurtosis (DK) MRI has been hindered largely by the long scan time required to sample over multiple b-values and/or diffusion-encoding directions. In this study, a novel method is described to expedite hybrid IVIM-DK imaging in the kidneys. Scan time is reduced by acquiring minimally-required non-zero b-values, while index calculation is made more time-efficient by using closed-form solution to replace nonlinear fitting. Experimental data demonstrated feasibility with b = 0/400/800/1600 s/mm2. Measurement variability was found greater among diffusion-encoding directions than between repeats, suggesting non-trivial structural anisotropy in the kidneys.