The modeling of the engine starting process is vital to ensure the successful start of the engine. However, the engine starting process is very complicated and challenging to model. To optimize the start model performance, an improved teaching-learning based optimization (ITLBO) algorithm is proposed. In ITLBO, a collective lesson preparation phase is increased to enhance the teaching ability of the teacher. The random learning phase is replaced by S-shape group learning, and students learn from the top students of their groups. Also the deterministic sampling selection phase is introduced to ITLBO, and the students with higher evaluation have more possibility to advance in class. The improved algorithm is tested on 18 benchmark functions. The results indicate that the proposed ITLBO algorithm performs much better in terms of convergence speed and accuracy than standard TLBO. When applied to the model adaptation of the turbofan engine starting process, ITLBO is used to optimize the speed line of the rotation components gradually from the lower speed line to the idle speed line. The weighted sum of relative errors between the model outputs and the start test data is taken as the fitness function. After adaptation, the maximum relative errors of model outputs to start test data are significantly decreased, which shows the effectiveness of the ITLBO in model adaption. INDEX TERMS Model adaptation, teaching-learning based optimization, collective lesson preparation, turbofan engine.