In this paper, we present a new approach to resolve linear weakly-singular partial integro-differential equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential equations into an partial differential equation. After that the fourth order compact finite difference scheme and collocation method is presented to obtain system of algebraic equations which solved to compute the unknown function. The efficiency and accuracy of the method is validated by its application to several distinct test problems which have exact solutions.