Based on fundamental theory of fracture mechanics and magnetic flux leakage using the virtual crack closure technique (VCCT) via the finite element modelling method, one type of magnetic-structural coupling algorithm which is suitable for single-and multi-crack growth will be proposed. Single-and multi-crack growth behaviour at different locations along circumferential and radial pipeline welds is also studied. After calculating crack incremental growth time with the above algorithm, the geometrical shape of cracks will be upgraded, the air mesh at the crack location is reconfigured. During expansion, automatic exertion of slight pressure increments of the load step, and crack growth calculation and magnetic field analysis will be also carried out iteratively. Six typical working conditions are applied as examples, of which the initial length lc is 2 mm. According to crack-opening distance, length of crack expansion, horizontal and vertical component peaks of magnetic induction intensity and other characteristic values describing crack growth, the damaged part and degree of damage to the pipeline weld was judged. Additionally, internal and external cracks, single and multiple pipeline cracks were also identified. The application of this algorithm can provide a theoretical basis for the research on crack growth of the pipeline weld.