To solve the multi-attribute decision-making （MADM） problem in which the weights of the attributes are unknown under linguistic Z-numbers environment， a novel decision-making method based on normal cloud model and preference ranking organization method for enrichment evaluation （PROMETHEE） method is proposed. Firstly， the conversion model based on linguistic scale function is proposed to convert linguistic Z-numbers to normal cloud models. Then， this paper defines a new cloud likelihood function， and utilizes the proposed function to establish a weight formula to measure the importance of each attribute in MADM. Moreover， a sine preference function is designed to acquire the preference values of alternatives， and the positive， negative and net flow on the basis of aggregated preference values can be calculated， and the corresponding ranking result of each alternative is acquired. Finally， the validity and feasibility of the proposed method can be illustrated by the problem of air pollution potential evaluation and comparative analysis with other existing three methods.