  Suppose ${\bf b}=\{b_n\}_{n=1}^{\infty}$ is a sequence of integers bigger
than 1 and ${\bf D}=\{{\mathcal D}_{n}\}_{n=1}^{\infty}$ is a sequence of
consecutive digit sets. Let $\mu_{{\bf b},{\bf D}}$ be the Cantor-Moran measure
defined by \begin{eqnarray*}
  \mu_{{\bf b},{\bf D}}&=& \delta_{\frac{1}{b_1}{\mathcal
D}_{1}}\ast\delta_{\frac{1}{b_1b_2}{\mathcal D}_{2}}\ast
\delta_{\frac{1}{b_1b_2b_3}{\mathcal D}_{3}}\ast\cdots.
  \end{eqnarray*}
  We prove that $L^2(\mu_{{\bf b},{\bf D}})$ possesses an exponential
orthonormal basis if and only if $\mu_{{\bf b},{\bf D}}\ast\nu={\mathcal
L}_{[0,N_1/b_1]}$ for some Borel probability measure $\nu$.
  This theorem shows that the generalized Fuglede's conjecture is true for such
Cantor-Moran measure. An immediate consequence of this result is the
equivalence between the existence of an exponential orthonormal basis and the
integral tiling of ${\bf D}_n={\mathcal D}_{n}+b_n{\mathcal D}_{n-1}+b_2\cdots
b_n{\mathcal D}_{1}$ for $n\geq1$.
