The significant frequency drift of integrated microwave photonic filters (IMPFs) is caused by relatively independent frequency fluctuations of the optical carrier and the photonic integrated filter, which imposes a rigid limitation on the practical application. In this paper, a novel method is proposed for suppressing the frequency drift of IMPFs. The scheme is implemented by utilizing an on-chip high-Q microring resonator as a frequency monitoring unit to track the instantaneous frequency drifts caused by the optical carrier drift and the temperature fluctuations of the photonic integrated chip. And the same frequency tuning is simultaneously applied on the photonic integrated filter to suppress the frequency drift of IMPFs based on the differential scheme. As a proof of concept, the proposed IMPF scheme is demonstrated on the Si3N4 platform, and the frequency drift is measured to be tens of MHz in one hour. Compared with conventional IMPF schemes, the frequency drift is significantly suppressed by 86.3% without using complex laser frequency stabilization and temperature control systems.