This paper present a method of straight path following for trenching works of underwater construction robot. First of all, deriving 3-DOF equation of underwater construction robot for an analysis of fundamental motion performance through a numerical simulation using Matlab. After then, the pure-pursuit method which is the one of the geometric path tracking method is introduced. When derailment of underwater construction robot from given the path is occurred by disturbances including obstacle, turning radius given from the pure-pursuit method will help underwater construction robot to follow the given path. The effectiveness of proposed method is verified through the numerical simulation.