The main purpose of this paper is to provide a method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrosophic linguistic numbers and the criterion weights are known. Firstly, the new operations and comparison method for simplified neutrosophic linguistic numbers are defined and some linguistic scale functions are employed. Subsequently, a Bonferroni mean operator and a normalized weighted Bonferroni mean operator of simplified neutrosophic linguistic numbers are developed, in which some desirable characteristics and special cases with respect to the parameters $p$ and $q$ in Bonferroni mean operator are studied. Then, based on the simplified neutrosophic linguistic normalized weighted Bonferroni mean operator, a multi-criteria decision-making approach is proposed. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing method to demonstrate the effectiveness and feasibility of the developed approach.