Abstract: This paper discusses a class of linear boundary value problem with conjugate value and a kind of shift for isotonic functional vector in Clifford analysis.Firstly,the author  gives some integral operators and tansform the problem into an integral equation problem.Applying the integral equation method and Schauder fixed-point theorem,the author proves the existence of the solution for the problem,and gives the integral representation of solution.

Key words: Clifford analysis, isotonic functional vector, linear boundary value problem