The high penetration of renewable energy into power grids introduces new challenges to the safe and stable operation of power systems. Existing short-circuit current calculation methods struggle to meet the speed requirements of modern power systems and often suffer from poor convergence as renewable energy penetration increases. This paper proposes a fault calculation method for power grids with high renewable energy integration, based on the adaptive combination of Newton and quasi-Newton methods. First, the influence of renewable energy control strategies on short-circuit current is analyzed, and an equivalent model for the steady-state fault condition of renewable energy sources is established. Then, to address the challenge of balancing computational speed and convergence in Newton-type iterative algorithms, non-convergence prediction and efficiency criteria are developed for renewable-rich scenarios. An adaptive selection mechanism is proposed to switch between Newton and quasi-Newton methods based on convergence and efficiency constraints, enabling accurate fault current computation. Finally, an improved IEEE33-bus test system with renewable energy integration is used for verification, and the results show that the proposed calculation method offers better performance in both computational speed and convergence than traditional methods.