Because of the inherent structural defects of P3P problem, the minimum solution method for calibration of 2D Lidar and camera has some shortcoming, such as poor numerical stability and accuracy. Aiming at the above problem, this paper proposes a robust minimum solution calibration method, which improves algorithm of P3P problem and the error measurement of optimal solution selection. Firstly, according to the P3P problem constructed by three checkerboards, the enhanced RP3P algorithm is used which can improve the stability of the solution. Secondly, an optimal solution selection strategy based on observation probability with uncertainty weighted is designed to improve the accuracy of the optimal solution. Experimental results show that the proposed algorithm can significantly improve the probability of reasonable solution and calibration accuracy compared with the algorithms in the literature. Under different noise levels, compared with Francisco method and Hu method, the probability of reasonable solution is improved by 5% ~ 41% and 2% ~ 20%, the rotation matrix accuracy is improved by 2° ~ 6° and 1. 5° ~ 2°, the translation vector accuracy is improved by 180 ~ 520 mm and 150~ 180 mm, so the performance is improved obviously.