The accurate measurement of depth of buried objects using GPR with a common-offset antenna (fixed distance between transmitter and receiver) requires two measurement parameters: (1) the GPR wave propagation velocity in the host material surrounding the buried objects; and (2) the two-way travel time when the GPR antenna is directly above the buried objects. Sham and Lai (2016) proposed a refined GPR wave travel path model in concrete when a cylindrical object is encountered. The model considers the factors of the object’s (or in this paper the underground pipe’s) radius and separation distance between the antenna transmitter and receiver. Based on this model, a constrained least-square (CLS) fitting method was applied in order to simultaneously address the trigonometrical, velocity estimation and two-way travel time components, thereby allowing the depth of the underground pipe to be calculated. One laboratory experiment in air and two sets of validation experiments in various soil environments were conducted. The results are also compared with those produced by point-based velocity measurement method (ASTM algorithm) (ASTM, 2011) and by normal least-square fitting method (Levenberg-Marquardt algorithm). The research has shown that: the proposed algorithm is low-cost in terms of calculation because no iteration and no convergency analysis is required; this algorithm is applicable to all the cases discussed here and is robust for GPR data with a certain degree of noise; this method helps to significantly reduce the percentage error of estimated depth from 10.0% (ASTM method) and 3.7% (L-M method) to 2.4% (CLS method) on average, while the discrepancy between estimated depth and actual depth can be reduced to the order of several centimeters. Based on an accurately estimated velocity, further work on host material characterization and water content measurement can then be conducted.