China’s education has entered the era of quality, and in order for higher vocational colleges to develop better, effective measures must be taken to improve the quality of education. Facing the continuous innovation of education in higher vocational colleges, it is necessary to strengthen institutional construction and constrain educational management with institutional constraints, which is the key to ensuring the education quality. The higher vocational education quality evaluation in the new era is regarded as multiple attribute decision-making (MADM). Recently, the EDAS and CRITIC model has been employed to solve MAGDM. The triangular fuzzy neutrosophic sets (TFNSs) are constructed as an efficient tool for portraying the uncertain information during the higher vocational education quality evaluation in the new era. In this paper, the triangular fuzzy neutrosophic number EDAS (TFNN-EDAS) model based on the Hamming distance and Euclid distance is constructed to solve the MADM under TFNSs. The CRITIC method is utilized to obtain the weight information based on the Hamming distance and Euclid distance under INNSs. Finally, a numerical example of higher vocational education quality evaluation in the new era is constructed and some efficient comparisons are founded to verify the TFNN-EDAS method.