  In this paper, we study the spectrality of a class of Moran measures
$\mu_{\mathcal{P},\mathcal{D}}$ on $\mathbb{R}$ generated by
$\{(p_n,\mathcal{D}_n)\}_{n=1}^{\infty}$, where
$\mathcal{P}=\{p_n\}_{n=1}^{\infty}$ is a sequence of positive integers with
$p_n>1$ and $\mathcal{D}=\{\mathcal{D}_{n}\}_{n=1}^{\infty}$ is a sequence of
digit sets of $\mathbb{N}$ with the cardinality $\#\mathcal{D}_{n}\in
\{2,3,N_{n}\}$. We find a countable set $\Lambda\subset\mathbb{R}$ such that
the set $\{e^{-2\pi i \lambda x}|\lambda\in\Lambda\}$ is a orthonormal basis of
$L^{2}(\mu_{\mathcal{P},\mathcal{D}})$ under some conditions. As an
application, we show that when $\mu_{\mathcal{P},\mathcal{D}}$ is absolutely
continuous, $\mu_{\mathcal{P},\mathcal{D}}$ not only is a spectral measure, but
also its support set tiles $\mathbb{R}$ with $\mathbb{Z}$.
