Abstract: For the full electromagnetic transient simulation of AC-(LCC)DC hybrid power grids, the involved numerical integration process would face frequent discontinuity problems. The most electromagnetic transient simulation mainly adopts the implicit trapezoidal integration method, but this type of implicit integration method is computationally inefficient when dealing with discontinuity problem. In order to solve this problem, this paper applies the Borel-Padé-Laplace (BPL) algorithm to the full-electromagnetic transient simulation of AC-(LCC)DC hybrid system, and a new kind of full-electromagnetic transient simulation method is proposed. Different from the traditional numerical integration methods, the BPL algorithm is a new class of asymptotic numerical methods that combines the Borel-Laplace transform with the classical Padé approximation. Taking the 3-machine 9-bus AC/DC system with 2 LCC-HVDC transmission lines as an example, the proposed method is tested against the simulation results of PSCAD/EMTDC. The test results show that the proposed method can completely avoid the problems faced by the traditional implicit integration method, and it has obvious advantages in computational efficiency.