Although the Landsat 30 m Enhanced Vegetation Index (EVI) products are important input variables in land surface models, recurring Landsat 5/7 EVI time series over cloud-prone, fragmented, and mosaic agricultural landscapes is still a great challenge. In this study, we put forward a simple, but effective “Light and Temperature-Driven Growth model and Double Logistic function fusion algorithm” (LTDG_DL). The empirical basis of the LTDG_DL algorithm was traced from the de Wit crop growth simulation model and the commonly observed nonlinear correlation between the EVI and the Leaf Area Index (LAI). It assimilates the ground daily solar radiation and air temperature to generate seasonal profiles of the empirical LAI and EVI and conducts the within-season calibration of the empirical EVI by adjusting crop growth using cloud-free Landsat EVI observations. The initial date of seedling emergence (DOYini) and the accumulated Growing Degree Days for completion of the vegetative and Flowering stage (FGDDs) were variables to which the algorithm’s accuracy was most sensitive. The variable-constrained optimization of the LTDG_DL algorithm was performed by loading the seedling emergence calendar of local prevailing crops and establishing an FGDD lookup table with an exhaustive sampling without replication method. Compared to temporal interpolation functions and Landsat–MODIS spatiotemporal fusion algorithms, the LTDG_DL algorithm had superior performance in the predictions of the EVI increment slope at the vegetative growth stage, the timing of the peak EVI, and the protection of key Landsat EVI observations over cloud-contaminated and complex landscape agricultural systems. Finally, the advantages and limitations of the LTDG_DL algorithm are discussed.