<p>The core of improving the comprehensive efficiency of laser cutting is to reduce the cost of cutting head transfer and piercing cost. This paper proposes a method based on the endpoint cutting problem model to connect multiple contours into a whole by considering the constrained connecting bridge to realize the uninterrupted cutting of multiple contours in one piercing and to reduce the length of the connecting bridge, and on the basis of which a cutting path planning method integrating the connecting bridge-air path is proposed, thus reducing the comprehensive cutting cost effectively. This method first analyzes and establishes an uninterrupted cutting optimization model considering the constraints of the contour features; then discretizes the contours according to the constraints to calculate the shortest distance between the contours and takes it as the feasible space for the length of connecting bridges; subsequently, an improved adaptive genetic algorithm is used to obtain the optimized global shortest connecting bridge positions and combinations that meet the constraints with the objective of fetching the minimum spanning tree; finally, by using the connecting bridge cutting method for planning the cutting path of the outer contour and determining the cutting sequence, coupled with the planning of the inner contour of the air path cutting trajectory, to achieve the purpose of integrating the reduction of transfer cost and piercing cost. Simulation results confirm the effectiveness and practicality of the proposed method.</p>