Cuckoo Search (CS) algorithm has shortcomings of weak local search ability, slow convergence speed, and low accuracy. In order to overcome these disadvantages, an improved CS algorithm based on Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (CS-BFGS) is proposed for solving inverse geometry heat conduction problems, and the physical field is the steady-state heat conduction. Firstly, the unknown initial boundary is evolved by Levy flights and elimination mechanism. Then the BFGS algorithm is applied to minimize the objective function. Finally, the influences of random errors, measurement point number, and measurement point position on the inverse results are investigated. The results show that the CS-BFGS algorithm has higher accuracy and faster convergence speed than BFGS and CS algorithm. With the decrease of measurement errors, the increase of measurement point number, and measurement point position closer to the inverse boundary, the results become more accurate.