The risky multi-criteria decision-making problem is studied, where the criteria values of the alternatives are twotuple linguistic and criteria weighted coefficient is completely unknown. By using the prospect theory and grey relation analysis approach, a decision-making approach based on the two-tuple linguistic prospect relational analysis is proposed. Firstly, the two-tuple linguistic positive and negative ideal solutions are determined and the corresponding two-tuple linguistic correlation coefficients are calculated. Then, the prospect decision-making matrix is constructed by calculating the two-tuple linguistic prospect value of each alternative, which is based on the positive and negative ideal solutions as the reference point. Furthermore, the criteria’s weighted coefficient based on the grey average relational degree is calculated. These alternatives can be ordered by comparing the two-tuple linguistic relative prospect grey relational degree. Finally, an example analysis shows the effectiveness of the proposed method.