An efficient strategy for dynamic crack propagation analysis is presented by combining the s-version of the finite element method (s-method) with Isogeometric analysis in a hybrid manner. In the conventional s-method, both global and local meshes are discretised using Lagrange finite elements [1,2]. While this enables flexible local refinement around a propagating crack tip, the assembly of global–local coupling matrices often requires specialised numerical integration (e.g., recursive subdivision) because global Lagrange shape-function derivatives are only piecewise smooth across element boundaries. The resulting increase in integration points can offset the computational benefits of the s-method. To address this bottleneck, we propose a hybrid s-version of the Isogeometric analysis strategy (hS-IGA), in which the global field is discretised using smooth B-spline bases, whereas the local mesh retains standard Lagrange elements to preserve a mature and validated crack-modelling framework. The enhanced inter-element continuity of the B-spline global basis renders the coupling-term integrands smoother within local elements, allowing standard Gauss quadrature to be used without recursive subdivision. A robust mapping procedure is introduced to evaluate global B-spline bases at local integration points for coupling-matrix assembly. Dynamic crack propagation is simulated in the local domain using a nodal force release technique consistent with a local fracture stress criterion, together with an appropriate crack representation scheme. Verification studies for stationary cracks and dynamic crack propagation demonstrate that the proposed hS-IGA maintains accuracy in near-tip stress evaluation while significantly reducing matrix-assembly cost, leading to improved overall efficiency compared with the conventional s-method and standard FEM at comparable accuracy levels.