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The object of the present paper is to generalize the Srivastava--Buschman's solution of the Convolution Integral Equation involving the Fox H-function kernel to the case of Generalized H-function kernel. There are some novel functions that form special cases of the generalized H-function but not Fox H-function. In the present paper, we shall give the solution of convolution equations involving two of such novel functions as kernels. Keywords and Phrases: Convolution integral equation, Generalized H-function (The [bar.H]-function), Laplace transform., 1. Introduction Srivastava and Buschman established the following theorem giving the solution of the Convolution integral equation whose kernel is Fox H-function. Theorem 1 (Srivastava and Buschman (5),(6)). The convolution [...]