  In this article, we deal with the order of growth of solutions of
non-homogeneous linear differential-difference equation \begin{equation*}
\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F(z), \end{equation*} where
$A_{ij},$ $F\left( z\right) $ are entire or meromorphic functions and $c_{i}$
$\left( 0,1,...,n\right) $ are non-zero distinct complex numbers. Under the
sufficient condition that there exists one coefficient having the maximal lower
order or having the maximal lower type strictly greater than the order or the
type of other coefficients, we obtain estimates of the lower bound of the order
of meromorphic solutions of the above equation.
