Recently, colleges/universities have paid a lot of attention to the teaching quality evaluation (TQE) of teachers in China. TQE is an essential way to improve teachers' teaching ability and quality in the teaching process. Then, the TQE of teaching supervisors is a multi-attribute decision-making (MADM) problem with vague, inconsistent, and indeterminate information. The simplified neutrosophic indeterminate set/element (SNIS/SNIE) is an appropriate form to express the indeterminate decision-making information in the TQE process. Therefore, this article presents an improved ranking method based on maximizing deviations principle and technique for order of preference by similarity (TOPSIS) for SNIS and applies it to evaluate teachers' teaching quality. First, the Hamming distance between two SNIEs is defined. Then, attribute weights are obtained by maximizing deviation method and the TOPSIS method-based decision-making model is developed for the MADM applications with unknown attribute weights. Finally, we perform the developed MADM model for a TQE case and compare it with existing related models to indicate the feasibility and rationality of the proposed model with unknown attribute weights in the SNIE circumstance.