Multi solution is a difficult problem in minimal solution method for extrinsic calibration of 2D laser radar and camera. This paper proposes three improvement measures for this problem and applies them to the minimum solution calibration process. Firstly, the observable spatial constraints of the sensor are used to eliminate the false solutions in which checkerboard cannot be observed by these sensors. Then, the error evaluation function of true solution selection is improved by using the constraint between the boundary laser points and boundary line segments. Finally, the least square solution of the translation parameters is solved by using chessboard boundary constraints. Simulation data and real data are tested in the experiment, and results show that the method can improve the hit rate of the true solution and calibration accuracy compared with Francisco method. When the noise variance of laser point is less than 20 mm, the hit rate of the true solution is about 98% , which meets the requirements of practical application. Compared with the traditional minimum solution calibration method, this paper uses checkerboard boundary constraints and observable spatial constraints to choose multiple solution sets, and optimizes the translation parameters. As a result, it can effectively improve the performance of the minimum solution calibration method.