Diffusional kurtosis imaging (DKI) is extended to double-pulsed-field-gradient (d-PFG) diffusion MRI sequences. This gives a practical approach for acquiring and analyzing d-PFG data. In particular, the leading d-PFG effects, beyond what conventional single-pulsed field gradient (s-PFG) provides, are interpreted in terms of the kurtosis for a diffusion displacement probability density function (dPDF) in a six-dimensional (6D) space. The 6D diffusional kurtosis encodes the unique information provided by d-PFG sequences up to second order in the b-value. This observation leads to a compact expression for the signalmagnitude, and it suggests novel data acquisition and analysis methods. Double-pulsed DKI (DP-DKI) is demonstrated for in vivo mouse brain with d-PFG data obtained at 7 T.