We give a new formula of the Laplace transform expressed using the delta derivative for the generalized time scales. This formula \[ Feft( z \right)_\mathds{T}= \mathscr{L}_{\mathds{T}} eft\{{feft( t \right)} \right\}eft( z \right) = ıt_0^ıfty {ze_{ minus eft( {z - 1} \right)} eft( {igma eft( t \right),0} \right)feft( t \right)\Delta t} \] combines the theory of classical Laplace and $\mathscr{Z}$ transforms. By choosing the time scale to be a set of real numbers, the classical Laplace transformation is obtained in a modified form, and if the time scale is chosen to be a set of integers, the classical $\mathscr{Z}$ transformation is obtained. Formulas for the Laplace transform of elementary functions, as well as formulas for real and complex shifting properties, are derived. These formulas are introduced for specific functions.