  Let $\mathcal{L}$ be the sub-Laplacian on H-type groups and $\phi:
\mathbb{R}^+ \to \mathbb{R}$ be a smooth function. The primary objective of the
paper is to study the decay estimate for a class of dispersive semigroup given
by $e^{it\phi(\mathcal{L})}$. Inspired by earlier work of Guo-Peng-Wang
\cite{GPW2008} in the Euclidean space and Song-Yang \cite{SY2023} on the
Heisenberg group, we overcome the difficulty arising from the
non-homogeneousness of $\phi$ by frequency localization, which is based on the
non-commutative Fourier transform on H-type groups, the properties of the
Laguerre functions and Bessel functions, and the stationary phase theorem.
Finally, as applications, we derive the new Strichartz inequalities for the
solutions of some specific equations, such as the fractional Schr\"{o}dinger
equation, the fourth-order Schr\"odinger equation, the beam equation and the
Klein-Gordon equation, which corresponds to $\phi(r)=r^\alpha$,
$r^2+r,\sqrt{1+r^2},\sqrt{1+r}$, respectively. Moreover, we also prove that the
time decay is sharp in these cases.
