This paper develops a forecasting technique by exponential smoothing applicable to nonlinear time series models such as a growing curve. It is assumed that the model equation can be approximated by the equation linearized in the vicinity of the preceding estimates of the coefficients. The derivation of the computing method resembles that of sequential linear least squares algorithms as the result of the linearization. The derived forecasting technique is characterized by the simplicity of computation and includes Brown's General Exponential Smoothing. Application to an exponential curve shows that the technique produces results acceptable for practical use.