The charge transport and accumulation in oil-paper can cause the insulation degradation. So far, the most widely used model to simulate space charge transport and accumulation is the bipolar charge transport (BCT) model, which can well simulate the space charge dynamics. However, there are two shortcomings in the algorithms for solving the BCT model. One is that there is almost no use of vectorisation technology, which may increase the complexity of the algorithm, the other is the usage of fixed step size which might bring extra computation cost. In view of this, an adaptive time-stepping transient upstream finite element method (FEM) is developed to solve the BCT model considering trapping/detrapping, as well as the recombination phenomenon under DC condition in this article. Then, a vectorisation technology is used in the method to optimise the algorithm. Moreover, the adaptive time-stepping method is introduced in simulation to reduce computation time and calculation amount. Simulation results are obtained by programing and later presented, which are basically consistent with the corresponding experimental results. Therefore, the proposed method is expected to promote the optimization design of the oil-paper insulation system.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.