Ultrasonic phased array testing is commonly employed for inspecting curved structures. Conventional plane wave imaging techniques, based on delay-and-sum in the time-domain, offer high image quality and inspection accuracy but suffer from low frame rates due to their high computational complexity. In this work, an efficient wavenumber-domain imaging method that combines non-stationary wavefield extrapolation and f-k migration is proposed for curved structure inspection. Special emission focal laws are designed to generate a sequence of steered plane waves through the curved interface. The raw data is then extrapolated to the top boundary of the region of interest, followed by f-k migration to reconstruct images with high time efficiency. Simulation and experimental evaluations demonstrate a time reduction by a factor of up to 32.24 compared to conventional time-domain plane wave image reconstruction with equivalent image quality, highlighting its potential for monitoring flaws in real-time.