Based on the bilevel multi-objective linear programming and the characteristic of grey system, the general gray bilevel multi-objective linear programming problem with its relevant definition and theorem are given. A globally convergent algorithm is given to solve the drifting grey bilevel multi-objective linear programming problem. Firstly, multi-objective programming is transformed into single programming by using linear plus power ideal point algorithm. Then, the grey bilevel linear programming can be transformed into a grey linear programming problem by its Kuhn-Tucker condition when the feasible domain is nonempty compact aggregate. So these problems can be solved by using the particle swarm optimization algorithm to obtain the solution of the gray bilevel multi-objective linear programming problem. Finally, an example shows the effectiveness of the proposed algorithm.