Numerical simulations employing the dynamic mesh method were performed to investigate the unsteady aerodynamics of variable-sweep wings during morphing. Quasi-steady and unsteady aerodynamic characteristics were compared, and the effects of key operating conditions (freestream velocity, angle of attack, morphing period, wingspan, chord length) on unsteady aerodynamics were analyzed. To enable the rapid prediction of unsteady aerodynamics, a Kriging surrogate model was established and validated against high-fidelity CFD results. The results indicate that unsteady effects manifest as hysteresis loops in aerodynamic coefficients within the morphing cycle. The wing morphing period, angle of attack, freestream velocity, and wingspan have a pronounced impact on the unsteady aerodynamic characteristics, whereas the effect of chord length is negligible. Reduced morphing periods, increased angles of attack, and increased wingspans amplify the hysteresis loop size and enhance the unsteady effects. An increase in the freestream velocity intensifies unsteady effects in the subsonic flow, while it attenuates unsteady effects in the supersonic flow. Compared to direct CFD simulations, the Kriging model for unsteady aerodynamic characteristics prediction achieves a 97% improvement in overall computational efficiency, while its predicted hysteresis loops are in good agreement with CFD results in both trend and magnitude, with an average prediction error below 4% and a maximum error of less than 6%. The Kriging surrogate model developed in this study offers substantial practical value for engineering applications by meeting the demand for rapid aerodynamic computation in the concept design phase for morphing aircraft.