As power systems are being highly stressed with the boost of loading levels and the introduction of new generation sources, transmission expansion planning (TEP) has regained its significance as a pivotal problem to be solved. To ameliorate the performance on both efficiency and accuracy for the solution of TEP from the aspect of algorithm design, a static DC TEP without generation redispatch is investigated by the proposed multi-group particle swarm optimisation (MGPSO) algorithm. MGPSO is based on the discrete PSO framework with several beneficial enhancements involved, such as Sobol sequence initialisation method, multi-group co-evolution strategy, and mutation mechanism. For the solution of linear programming subproblem within the framework of MGPSO, a linear equation system is extracted and then addressed with efficient LU decomposition approach. Case studies have been implemented on five classical benchmarks, ranging from 6-bus to 118-bus, between the MGPSO and commercial software Lingo 11.0 to validate the superiority of MGPSO. Speedup analysis as well as performance evaluation of different acceleration strategy involved in MGPSO are implemented and discussed.