Quasi-periodic pulsations (QPPs), which carry time features and plasma characteristics of flare emissions, are frequently observed in light curves of solar/stellar flares. In this study, we investigated non-stationary QPPs associated with recurrent jets during an M1.2 flare on 2022 July 14. A quasi-period of ∼45±10 s, determined by the wavelet transform technique, is simultaneously identified at wavelengths of soft/hard X-ray and microwave emissions, which are recorded by the Gravitational Wave High-Energy Electromagnetic Counterpart All-sky Monitor, Fermi and the Nobeyama Radio Polarimeters, respectively. A group of recurrent jets with an intermittent cadence of about 45 ± 10 s are found in the Atmospheric Imaging Assembly (AIA) image series at 304 Å, but they are 180 s earlier than the flare QPP. All observational facts suggest that the flare QPPs could be excited by recurrent jets, and they should be associated with non-thermal electrons that are periodically accelerated by a repeated energy release process, such as repetitive magnetic reconnection. Moreover, the same quasi-period is discovered at double footpoints connected by a hot flare loop in AIA 94 Å, and the phase speed is measured to be ∼1,420 km s−1. Based on the differential emission measure, the average temperatures, number densities, and magnetic field strengths at the loop top and footpoint are estimated to be ∼7.7/6.7 MK, ∼7.5/3.6 × 1010 cm−3, and ∼143/99 G, respectively. Our measurements indicate that the 45-s QPP is probably modulated by the kink-mode wave of the flare loop.