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• Cross evaluation is introduced into environmental performance evaluation based on DDF. • A cross-direction evaluation method considering undesirable outputs is proposed. • A new direction vector scanning method based on polar coordinates is developed. When using directional distance function (DDF) for efficiency evaluation, each decision-making unit tends to choose the direction that maximizes its own efficiency for evaluation, which may cause the efficiency score to be overestimated and unrecognized by others. This paper is concerned with the fair evaluation of the DDF in data envelopment analysis. The concept of cross evaluation is introduced into the environmental performance evaluation based on DDF, and then a new cross-direction evaluation method considering undesirable outputs is proposed. In addition, we propose a new direction vector scanning method based on polar coordinates to realize the peer-evaluation of efficient decision-making unit. Finally, our approach is applied to analyze the transportation industry. [ABSTRACT FROM AUTHOR]