Performance assessment of teaching competency plays an important role in educational activities. Previous assessments of lecturers’ performance have failed to distinguish between potential capacity and their teaching effectiveness. To solve this problem, the integrated approach of quantitative assessment and multi-criteria decision-making models has become one of the main trends for assessing the performance of lecturers in multiple dimensions: self, peer-, manager- and student-based evaluation. This paper proposes a novel hierarchical approach, developed by the Technique for Order preference by Similarity to Ideal Solution method in an interval-valued complex neutrosophic set environment, to more accurately and comprehensively understand the evaluation process and fit it into a systematic framework. An application is given to illustrate a practical solution in lecturer’s evaluation. The accuracy of the proposed method is verified by comparing with other methods.