© 2018, Emerald Publishing Limited.Purpose: Evaluations of grey systems and systems with subjective judgements are always like an impasse for science and companies. Especially, calculations of the problems which include various units are really difficult situations. The purpose of this paper is to propose a grey analytic hierarchy process (G-AHP) for engineering and managerial problems with grey systems to make more clear and objective decisions. Design/methodology/approach: Proposed G-AHP approach is applied to project manager selection for a software project of an energy company. The application includes three different units as year, score and assessment. Six engineers are evaluated with 25 criteria in the application. Weights of the factors and assessments are done by three top managers of the company as pairwise comparisons. Other data in the decision matrix are obtained from the personal information and exam results of engineers. Findings: Final weights of the criteria and evaluations of engineers are all done with the proposed G-AHP. Obtained results of G-AHP are also compared with grey “VlseKriterijumska Optimizacija I Kompromisno Resenje” results as a validation of the calculations and proposed approach. Final results of the applications are ranked for the evaluations and comparison. All results of the case study are concluded with the effectiveness and applicability of the proposed G-AHP method both for this study and other fields of science, engineering and management. Originality/value: This study provides to evaluate and interpret grey systems with different units and subjective judgements for science, engineering and management more clearly and objectively in an easier way.