This paper provides an OpenMP-based parallel Very Dishonest Newton (VDHN) algorithm with variable step size, running transient stability simulations (TSA) on multi-core computers. Under the framework of simultaneous solution method of TSA, the step-size control strategy is used according to the local truncation error theory firstly. Then, computation of the generation units, which is the most time-consuming part of the simulation, is dynamically dispatched to several cores using an α dynamic scheduling scheme to obtain workload balancing based on OpenMP. Due to the convergence of Newton-type iterations, an adaptive Jacobian update control strategy is applied to reduce the sequential part of the simulation and the overhead generated by OpenMP. Several large scale test cases verify the validity and practicability of the proposed parallel algorithm, showing that the proposed approach achieves high speed-up and a considerable reduction in parallel overheads.