Abstract The star formation history (SFH) is a key issue in the evolution of galaxies. In this work, we developed a model based on a Gaussian and gamma function mixture to fit SFHs with varying numbers of components. Our primary objective was to use this model to reveal the shape of SFHs and the corresponding physical driving factors. Specifically, we applied this model to fit SFHs from the TNG100-1 simulation. Our study led to the following findings. (1) Our model fits with TNG star formation histories well, especially for high-mass and red galaxies; (2) a clear relationship exists between the number and shape of fitted components and the mass and color of galaxies, with notable differences observed between central/isolated and satellite galaxies. (3) Our model allows us to extract different episodes of star formation within star formation histories with ease and analyze the duration and timing of each star formation episode. Our findings indicate a strong relationship between the timing of each star formation episode and galaxy mass and color.