Context. Kink oscillations, which are often associated with magnetohydrodynamic waves, are usually identified as transverse displacement oscillations of loop-like structures. However, the traveling kink oscillation evolving to a standing wave has rarely been reported. Aims. We investigate the traveling kink oscillation triggered by a solar flare on 2022 September 29. The traveling kink wave is then evolved to a standing kink oscillation of the coronal loop. Methods. The observational data mainly come from the Solar Upper Transition Region Imager (SUTRI), Atmospheric Imaging Assembly (AIA), and Spectrometer/Telescope for Imaging X-rays (STIX). In order to accurately identify the diffuse coronal loops, we applied a multi-Gaussian normalization (MGN) image processing technique to the extreme ultraviolet (EUV) image sequences at SUTRI 465 Å, AIA 171 Å, and 193 Å. A sine function within the decaying term and linear trend is used to extract the oscillation periods and amplitudes. With the aid of a differential emission measure analysis, the coronal seismology is applied to diagnose key parameters of the oscillating loop. At last, the wavelet transform is used to seek for multiple harmonics of the kink wave. Results. The transverse oscillations with an apparent decay in amplitude and nearly perpendicular to the oscillating loop are observed in the passbands of SUTRI 465 Å, AIA 171 Å, and 193 Å. The decaying oscillation is launched by a solar flare erupted close to one footpoint of coronal loops and then it propagates along several loops. Next, the traveling kink wave is evolved to a standing kink oscillation. The standing kink oscillation along one coronal loop has a similar period of ∼6.3 min at multiple wavelengths, and the decaying time is estimated at ∼9.6-10.6 min. Finally, two dominant periods of 5.1 min and 2.0 min are detected in another oscillating loop, suggesting the coexistence of the fundamental and third harmonics. Conclusions. First, we report the evolution of a traveling kink pulse to a standing kink wave along coronal loops that has been induced by a solar flare. We also detected a third-harmonic kink wave in an oscillating loop. © 2023 EDP Sciences. All rights reserved.