Periodic interference frequently affects the measurement of small signals and causes problems in clinical diagnostics. Adaptive filters can be used as potential tools for cancelling such interference. However, when the interference has a frequency fluctuation, the ideal adaptive-filter coefficients for cancelling the interference also fluctuate. When the adaptation property of the algorithm is slow compared with the frequency fluctuation, the interference-cancelling performance is degraded. However, if the adaptation is too quick, the performance is degraded owing to the target signal. To overcome this problem, we propose an adaptive filter that suppresses the fluctuation of the ideal coefficients by utilizing a $\frac{\pi}{2}$ phase-delay device. This method assumes a frequency response that characterizes the transmission path from the interference source to the main input signal to be sufficiently smooth. In the numerical examples, the proposed method exhibits good performance in the presence of a frequency fluctuation when the forgetting factor is large. Moreover, we show that the proposed method reduces the calculation cost.