Abstract: It is a common practice for domestic researchers to conduct Computational Fluid Dynamics (CFD) simulations of the aircraft gust response using the field velocity method (FVM). The more accurate split velocity method (SVM) proposed recently has become progressively popular for gust response analysis but is limited to rigid aircraft. This paper extends SVM to simulate the One-Minus-Cosine gust response of elastic airfoils and to alleviate the gust load. First, velocity fields obtained by solving unsteady Navier-Stokes equations in dynamic meshes are decomposed into the gust and background velocities. The control equations of SVM are derived, which show that FVM is an approximation of SVM when neglecting the source term. Next, the CFD/CSD coupling algorithms in the time domain are established for the elastic airfoil gust response prediction and the gust response alleviation based on pitch control. The One-Minus-Cosine gust responses of rigid and elastic NACA0012 airfoils agree well with the reference data. The effects of gust length, viscosity, and structural elasticity on gust response are also analyzed. Finally, the One-Minus-Cosine gust alleviation simulation of the elastic NACA64A010 airfoil is conducted. Results show that changing only the plunge speed is more efficient in alleviating the peak gust load; the combined control of plunge speed and pitch angle can alleviate the plunge and pitch movements. This work lays a foundation for further study on gust response and alleviation of three-dimensional aircraft.