Harmonic analysis of time series is an important technique in remote sensing to reveal seasonal land surface dynamics. However, frequency selection in the harmonic analysis is often difficult because high-frequency components are useful for delineating seasonal dynamics but sensitive to noise and gaps in time series. On the other hand, it is challenging to obtain temporally continuous satellite data with high quality because of atmospheric contamination. We developed a novel regression method named Harmonic Adaptive Penalty Operator (HAPO) for harmonic analysis of unevenly distributed time series. We introduced a new penalty function to minimize unexpected fluctuations in the model, which can substantially reduce the overfitting issue of regression in time series with temporal gaps. Specifically, the new penalty function minimizes the length of the model curve and the value range difference between the model and the time series observations. We compared HAPO with three widely used regression methods (OLS: Ordinary Least Squares; LASSO: Least Absolute Shrinkage and Selection Operator; and Ridge) in different scenarios using Landsat time series data across the United States. First, we evaluated methods using the Landsat surface reflectance time series within a single year. HAPO showed low and consistent monthly Root Mean Square Deviation (RMSD) values, in which most of the time RMSD of predicted reflectance were less than 0.04. More importantly, HAPO showed consistent and less bias given varying density and irregularity of time series. Second, we evaluated methods using multi-year time series. HAPO was a better predictor of relatively short time series (< 4 years) with steady low RMSD values. When a longer time series ( 4 years) was used, all four methods showed similar RMSD values, but HAPO outperformed the other methods if there were temporal gaps. Therefore, for places with large seasonal observation gaps or for time series that are relatively short (less than 4 years), HAPO can provide more consistent and accurate results in harmonic analysis of time series.