Abstract: Presents on non-numerical algorithm for solving 2-dimensional linear programming problems with its basic idea in divide-and-conquer. It can divide the astriction condition into different dasses according to the straight slope and the truncated distance on the x and y-axis, and then remove the redundant redundant restrictive conditions such that the computation is much simplified . This algorithm requiresO(n2) comparisons and O(n2) arithmetic operations.