This paper is devoted to frequency estimation of a sinusoidal signal with a time-varying amplitude. The amplitude can take zero values, but should be known and bounded. The first order linear regression model is obtained. The estimation algorithm has been constructed basing on standard gradient approach. It is shown that the frequency estimation error converges to zero exponentially fast. The described algorithm does not require measuring or calculating derivatives of the input signal. The efficiency of the proposed approach is demonstrated through a set of numerical simulations.