The objective of this paper is to establish a generalization of the triple Laplace transform, and the other triple integral transforms available in the class of Laplace transform called the new modified triple integral transform. In this paper we have proved all the fundamental properties like linearity property, first shifting property, second shifting property, change of scale property, derivative property, periodic property, etc., for the new modified triple integral transform. The applicability of this transform is demonstrated by using this new integral transform for solving partial differential equations and partial integro-differential equations.