  In this article, a large class of simple modules over the
Schr\"odinger-Virasoro algebra $\mathcal{G}$ are constructed, which include
highest weight modules and Whittaker modules. These modules are determined by
the simple modules over the finite-dimensional quotient algebras of some
subalgebras. Moreover, we show that all simple modules of $\mathcal{G}$ with
locally finite actions of elements in a certain positive part belong to this
class of simple modules. Similarly, a large class of simple modules over the
$W$-algebra $W(2,2)$ are constructed.
